EARTH   SGMlUggS  LI  BR ARV 


BERKELEY 

LIBRARY 

UNIVERSITY  Of 


UftXAHV 

ARTHUR  6.  KAKI.K 

b  Ca'iW 


CHEMICAL   CRYSTALLOGRAPHY 


AN    INTRODUCTION    TO 

CHEMICAL  CRYSTALLOGRAPHY 


BY 

P.    GROTH 


PROFESSOR  OF   MINERALOGY   AND   CRYSTALLOGRAPHY   IX  THE   UNIVERSITY   OF  MUNICH 


AUTHORISED     TRANSLATION 


HUGH  MARSHALL,  D.Sc.,  F.R.S. 

LECTURER   ON   CHEMISTRY  AND  ON   MINERALOGY  AND  CRYSTALLOGRAPHY 
IN  THE   UNIVERSITY   OF  EDINBURGH 


NEW   YORK 
JOHN    WILEY  &   SONS 

43-45  EAST  NINETEENTH  STREET 
1906 


Ool.  dept 
Printed  in  Great  Britain 


PREFACE 

Ix  this  short  treatise  on  general  chemical  crystallography 
the  attempt  has  been  made  to  present  the  hitherto  recog- 
nised relations  between  the  properties  of  crystallised  sub- 
stances and  their  chemical  constitution  on  the  basis  of  a 
definite  view  regarding  the  structure  of  crystals.  In  doing 
so,  a  knowledge  of  the  crystallographical  laws  is  assumed, 
to  an  extent  corresponding  to  the  elementary  treatment 
of  them  as  contained  in  my  text  book,  Physikalische 
Krystallographie,  now  appearing  in  its  fourth  edition  ;  for 
information  regarding  the  terms  here  employed,  and  also 
for  a  fuller  introduction  to  the  theory  of  crystal  structure, 
together  with  the  geometrical  ideas  requisite  thereto,  the 
reader  is  referred  to  the  above  work.  In  order  to  secure  a 
maximum  of  conciseness  and  brevity  in  the  treatment,  it 
has  been  necessary  to  forego  entering  more  fully  into  the 
different  views  which  at  various  times  have  been  propounded 
regarding  the  matter  in  question.  Anyone  who  wishes 
information  regarding  the  history  of  the  development  of 
chemical  crystallography,  will  find  a  short  historical  treat- 
ment of  the  subject  in  Section  III.  of  the  Introduction  to 
Chemical  Crystallography,  by  A.  Fock  (Leipzig,  1888),  and 
especially  in  the  extended  English  version  of  the  same  work, 
by  W.  J.  Pope  (Oxford,  1895)  ;  there  is  a  detailed  and 
complete  statement  in  the  excellent  work  by  A.  Arzruni, 
Physikalische  Chemie  der  Krystalle  (Brunswick,  1893),  which 
also  constitutes  Part  I.  of  Graham-Otto's  Ausfiihrliches 
Lehrbuch  der  Chemie.  Subsequent  investigations  in  this 
field  are  contained  in  the  various  volumes  of  the  Zeitschrift 

819490  0? 


vi  PREPACK 

.tallQgraphic,  partly  in  the  form  of  original  contribu- 
tions, partly  as  abstracts. 

The  investigation  of  the  dependence  of  the  properties 
of  crystallised  substances  on  their  chemical  nature  naturally 
belongs  to  the  domain  of  physical  chemistry,  whose  vota- 
ries, however,  during  the  period  of  the  rapid  develop- 
ment of  this  branch  of  science,  have  busied  themselves 
chiefly  with  the  study  of  amorphous  substances  (and 
especially  of  solutions).  Only  quite  recently  have  they 
begun  to  turn  their  attention  to  crystallised  substances, 
and  numerous  investigations  have  been  published,  particu- 
larly concerning  so-called  "mixed  crystals,"  but  mostly 
confined  to  theoretical  deductions  from  the  phase  rule, 
or  to  the  determination  and  discussion  of  fusion  curves. 
However  valuable  such  investigations  may  be,  they  can 
never  take  the  place  of  the  exact  examination  of  the  crystal- 
lisation products  themselves  (as  is  evident  from  the  fact 
that  substances  have  been  designated  as  "  isomorphous " 
merely  on  the  evidence  of  the  fusion  curves  of  their  mix- 
tures, even  although  nothing  was  known  regarding  their 
crystallographical  relationships).  This  arises  from  the 
circumstance  that  the  laws  observed  with  amorphous 
substances  cannot  be  directly  applied  to  crystallised  sub- 
stances, which  are  essentially  so  different  from  them  ;  and 
especially  from  the  fact  that  many  things  of  totally  distinct 
nature,  whose  differentiation  still  requires  further  investiga- 

:i,  are  thrown  together  under  the  name  of  "solid  solu- 
tions." The  physical  crystallographical  methods  necessary 
for  this  have  in  recent  times  been  so  perfected  that,  in 
order  to  shed  light  on  these  matters,  only  their  general 
employment  on  the  part  of  physical  chemists  is  necessary  ; 
and  it  is  an  additional  aim  of  this  book  to  discuss  the 
vantage  points  whence,  as  the  result  of  further  investiga- 
tion, there  might  open  up  the  prospect  of  substituting  for 
the  mere  i-nUtcd  relationships  which,  so  far,  have  been 
observed  to  exist  between  the  crystal  properties  and  the 
chemk.il  «»i^titution  of  substam  es,  the  recognition  of  some 


PREFACE  vii 

general  law — a  goal  whose  attainment  will  certainly  be 
made  distinctly  easier  by  the  great  advances  which  the 
theoretical  investigation  of  crystal  structure  has  made  in 
recent  times.  Bearing  these  points  in  mind,  chemical 
crystallography  should  constitute  one  of  the  most  highly 
favoured  and  profitable  fields  of  research  in  the  whole 
domain  of  physical  chemistry. 

In  conclusion,  it  may  be  remarked  that  the  present  work 
at  the  same  time  forms  a  forerunner  to  a  systematic  and 
critical  digest  of  the  now-existing  researches  on  the  crystal 
forms  and  other  physical  properties  of  crystallised  substances, 
which  for  a  series  of  years  I  have  been  preparing.  For  this 
work  the  Royal  Academies  of  Sciences  in  Vienna,  Berlin, 
Leipzig,  and  Munich  have  in  recent  years  placed  at  my 
disposal  assistance  in  the  persons  of  Dr  Gossner  and  Dr 
Hlawatsch  ;  to  these  must  also  be  added  Dr  Steinmetz, 
whose  research,  frequently  mentioned  in  this  work,  will 
shortly  be  published.  As  a  result  of  this  assistance,  it  has 
been  possible  so  to  advance  the  preparations  that  the  print- 
ing of  the  work  will  soon  be  commenced. 

P.  GROTH. 

MUNICH,  September  1904. 


TRANSLATOR'S    NOTE 

THIS  translation  of  Groth's  Einleitung  in  die  chemische 
Krystallographic  has  been  prepared  with  the  co-operation 
of  the  author,  who  has  made  several  alterations  rendered 
necessary  by  investigations  which  have  been  published  in 
the  interval  between  the  appearance  of  the  original  and 
the  completion  of  the  translation  ;  he  has  also  kindly  read 
the  proof-sheets. 

The  translator's  endeavour  has  been  to  adhere  as  closely 
as  possible  to  the  original  in  all  respects  ;  consequently,  as 
the  latter  is  intentionally  a  very  condensed  statement  of 
the  subject,  this  character  may  appear  even  more  markedly 
in  the  translation. 

In  order  to  render  the  book  more  readily  useful  to 
English-speaking  students,  additional  references  have  been 
given,  when  possible,  to  abstracts  (or,  in  some  cases,  to 
original  papers)  appearing  in  the  Journal  of  the  Chemical 
Society.  Considerable  assistance  in  providing  these  refer- 
ences, and  in  reading  proofs,  has  been  kindly  rendered  by 
Mr  A.  T.  Cameron,  M.A. 

CHEMISTRY  DEPARTMENT, 

UNIVERSITY  OF  EDINBURGH. 


CONTENTS 

PAOK 

Crystal  Structure  and  its  Possible  Varieties  i 

Polymorphism.  .  .  .  .  .  .  .16 

The   Comparison  of  the  Crystal  Structures  of  Chemically  Allied 

Substances  (Morphotropy)          .....         36 

Isomorphism — 

A.  Similarity  of   Crystal   Structure   in    Substances   possess- 

ing Analogous  Chemical  Constitution  .  .  .66 

B.  Relations  between  Crystals  and  Solutions  of  Isomorphous 

Substances  .  .  .  .  .  .86 

C.  Isomorphous  Mixtures        .            ....  88 
Polymorphous  Transformations  of  Isomorphous  Mixtures  99 
The  Crystalline  Forms  of  Isomorphous  Mixtures  .            .  100 
Optical  Properties  of  Isomorphous  Mixtures           .            .  102 

Molecular  Compounds  ......       105 

Racemic  and  Optically  Active  Compounds   .  .  .108 

Index  .  .  .  .  .  .  .  .  .119 


CRYSTAL     STRUCTURE     AND     ITS 
POSSIBLE    VARIETIES 

THE  molecular  hypothesis  of  matter  assumes  that  in  solid 
bodies  the  movements  of  the  molecules  are  limited  about 
certain  positions  of  equilibrium,  which  are  permanently 
vacated  only  under  the  influence  of  external  forces.  In  a 
crystallised  substance  the  positions  of  equilibrium  must  be 
characterised  by  a  regular  arrangement  in  space,  and  this 
arrangement  is  called  the  crystal  Structure  of  the  sub- 
stance. 

Physical  crystallography,  on  the  one  hand,  teaches  us 
that  the  sum  total  of  the  regularities  which  affect  the  shape 
and  the  other  physical  properties  of  crystals  can  be  deduced 
only  by  means  of  a  general  and  complete  theory  of  crystal 
structure  ;  and,  on  the  other  hand,  it  shows  how,  from  a 
knowledge  of  these  properties,  conclusions  may  be  drawn 
with  regard  to  the  crystal  structure  of  a  substance.  This 
necessitates  not  only  a  knowledge  of  the  optical  properties, 
the  cohesion  relationships,  etc.,  of  the  particular  substance, 
but  also,  and  more  especially,  a  very  thorough  knowledge 
of  the  complete  assemblage  of  crystal  faces  pertaining  to  it 
(crystallising  it  under  as  widely  different  conditions  as 
possible),  so  as  to  be  able  to  determine  which  of  the  possible 
faces  of  the  assemblage  are  the  most  favoured,  under  all 
conditions,  with  regard  to  development,  i.e.,  which  of  them 

\ 


nii'.MU  AI.  (  RYSTALLOGHAl'liy 

coincide  with  the  principal  planes  of  the  regular  structure. 
If  these  faces  are  adopted  as  the  fundamental  planes  for  the 
proper  orientation  of  the  crystal,  then  the  ratios  of  its 
primitive  parameters  are  at  the  same  time  proportional  to 
the  relative  distances  of  the  positions  of  equilibrium  along 
the  principal  directions  in  the  crystal.  There  is  thus 
obtained  a  representation  of  the  internal  structure  of  the 
crystallised  substance,  which  allows  of  the  known  properties 
of  the  substance  being  deduced  from  this  structure  ;  and 
although  we  are  still  in  ignorance  as  to  the  nature  of  the 
internal  forces1  acting  on  the  molecules,  we  are  justified, 
nevertheless,  in  assuming  that  the  arrangement  thus  found 
represents  that  of  the  positions  of  equilibrium  with  regard 
to  these  forces. 

Since  the  equilibrium  in  a  crystal  structure  is  dependent 
on  the  state  of  motion  of  the  material  particles,  the  stability 
of  this  equilibrium  must  necessarily  vary  with  the  tempera- 
ture. Since,  further,  every  structure  may  possess  several 
positions  of  equilibrium  (but  these  of  different  degrees  of 
stability),  it  follows  that  it  is  only  within  a  certain  range  of 
temperature  (constancy  of  pressure  being  assumed)  that  any 
one  particular  crystal  structure  represents  the  most  stable 
amongst  the  kinds  of  equilibrium  which  are- possible  ;  out- 
side this  range  other  kinds  of  arrangement  possess  more 
stable  equilibrium.  If  the  boundary  between  two  such 
neighbouring  ranges  of  temperature  is  transgressed,  then 
the  crystal  structure  hitherto  possessed  by  the  substance 
may  indeed  continue  to  correspond  to  a  state  of  stable 
equilibrium,  but  this  no  longer  possesses  the  highest  degree 
of  stability  possible.  Consequently,  under  certain  circum- 
;iices,  there  takes  place  a  transformation  into  what  is  now 
the  more  stable  condition,  and  there  results  a  different 
modification  «»f  the  substance,  with  different  crystal 
icture  and  correspondingly  different  physical  properties 

1  Lord   Kelvin   (/V/i/.    .J/^.    1902,   4,    139  et  seg.~)    h:is  attempted   to 
deduce  theorct  .  ;mption?,  the  possibility  of 

ious  arrangement  'c  equilibrium. 


CRYSTAL  STRUCTURES  3 

— there  has  taken  place  a  discontinuous  change  of  the 
vectorial  properties  and  also,  in  general,  of  the  scalar 
properties  of  the  substance.1 

This  property  of  substances,  to  assume  different  crystal 
structures  (and,  consequently,  different  crystalline  forms) 
under  different  conditions,  is  called  polymorphism  or 
physical  isomerism,  and  the  different  states  of  a  sub- 
stance are  said  to  be  polymorphous  modifications  of 
that  substance.  Since  these  states  differ  only  in  crystal 
structure  (with  all  that  that  implies),  the  differences  dis- 
appear as  soon  as  the  substance  is  changed  into  the  amor- 
phous state — whether  by  fusion,  dissolution,  or  vaporisation. 
Should,  thereafter,  differences  still  persist,  then  they  must 
be  due  to  differences  of  structure  within  the  molecules  from 
which  the  crystals  were  formed,  so  that  the  case  is  then  one 
of  chemically  isomeric  substances.  The  crystal  struc- 
tures of  two  chemically  isomeric  substances  are  different, 
just  as  those  of  two  polymorphous  modifications  of  one 
substance  are. 

In  both  cases,  however,  there  may  exist  certain  similarities 
between  the  crystalline  forms,  and  since  the  general  laws  regula- 
ting the  relations  between  the  crystalline  forms  of  polymorphous 
substances  and  of  isomeric  substances  have  not  yet  been  clearly 
made  out,  it  is  not  possible,  from  any  mere  difference  in  the 
crystal  structure  of  two  substances  possessing  the  same  chemical 
composition,  to  decide  whether  these  are  physically  or  chemically 
isomeric. 

If,  however,  the  two  substances  react  differently  after  they  are 
fused,  dissolved,  or  vaporised,  the  discrimination  between  the  two 
cases  becomes  indubitable,  for  then  the  substances  must  be  chemi- 
cally isomeric,  or  polymeric.  There  are,  however,  chemically  iso- 
meric substances  which  so  readily  undergo  transformation,  the  one 
into  the  other,  that  they  yield  identical  products  when  they  are 
fused,  dissolved,  or  vaporised ;  and  in  such  a  case  it  is  also 
possible  that  the  crystals  of  the  one  isomer  may  grow  in  the 

1  A  change  of  pressure,  as  of  temperature,  likewise  affects  the  equili- 
brium conditions,  and  in  accordance  with  this  fact,  Tammann  has  succeeded 
in  proving  the  occurrence  of  transformations  into  modifications  which  were 
previously  unknown,  as,  for  example,  in  the  case  of  ice  and  of  phenol. 


4  CHEMICAL  CRYSTALLOGRAPHY 

liquid^  solution,  or  vapour  obtained  from  the  other,  just  as  the 
crystals  of  one  polymorphous  modification  may  grow  in  the  liquid, 
solution,  or  vapour  obtained  from  some  other  modification  of  the 
same  substance. 

A  characteristic  of  polymorphous  modifications  of  one  sub- 
stance is  their  transformability,  the  one  into  the  other,  without 
having  undergone  fusion  or  evaporation,  and  without  the  inter- 
vention of  a  solvent,  but  merely  on  change  of  temperature.  This 
direct  transformation  from  one  state  of  crystallisation  into  another  can 
be  recognised  with  the  greatest  certainty  by  means  of  O.  Lehmann's 
"crystallisation  microscope,"  which  makes  it  possible  to  study  the 
behaviour  of  a  preparation  while  it  is  being  subjected  to  changing 
temperatures.1  Since  two  polymorphous  modifications  differ  from 
one  another  as  regards  the  forms  in  which  they  grow,  their  optical 
properties,  etc.,  the  formation  of  a  new  modification  during  a 
change  of  temperature  can  be  at  once  detected  (very  easily  so 
with  crossed  nicols,  should  one  of  the  two  modifications  be  singly 
refracting) ;  at  the  same  time  it  is  possible  to  determine  which  of 
the  modifications  is  the  stable  one  at  any  given  temperature,  since 
it  grows  at  the  expense  of  the  other.  In  this  way  O.  Lehmann  has 
proved  the  existence  of  various  polymorphous  modifications  fcr 
a  large  number  of  substances.2 

The  crystallisation  microscope  can  also  be  used  with  advantage 
for  the  solution  of  the  question  whether  the  isomerism  between  two 
substances  is  chemical  or  physical.  For  this  purpose  one  of  the 
two  is  fused  on  an  object  glass,  and  during  the  cooling  of  the  fused 
mass  small  crystals  of  the  respective  substances  are  brought  into 
contact  with  it  at  two  different  points.  Should  both  crystals  grow 
into  the  fused  mass  until  they  meet,  and  thereafter  one  of  these 
crystallisations  continue  to  grow  at  the  expense  of  the  other 
(renewed  heating  being  requisite  in  some  cases),  then  the  crystals 
under  investigation  are  two  polymorphous  modifications  of  the 

i-  substance.  Should,  however,  only  one  of  the  crystals 
employed  for  "inoculation"  grow  into  the  fused  mass  when 
brought  in  contact  with  it,  or,  in  the  event  of  both  growing,  should 

1  Concerning  this  instrument,  see  O.  Lehmann's  Molekularphysik, 
Leipzig,  1888, 1.  133^/^7.  ;  alsohis  Krystallanalyst^  Leipzig,  1891  ;  further, 
Groth's  Fhytikaluche  Krystallographit,  3rd  edition,  1895,  753  et  seq. ;  41!) 
edition,  1905,  786.  » 

a  See  his  Molikularphyiik,  nn<l  numerous  contributions  to  the  /tils,  f. 


CRYSTAL  STRUCTURES  5 

the  two  resulting  crystallisations  remain  indifferently  side  by  side 
when  they  meet  (even  after  the  temperature  is  raised),  then  the 
two  substances  must  be  considered  as  chemically  isomeric.  The 
alteration  of  the  temperature  is  necessary  owing  to  the  fact  that 
the  rate  of  transformation  of  polymorphous  substances  may  be 
very  small  at  low  temperatures,  so  that  in  many  cases  both  forms 
can  exist  in  contact  with  one  another  even  for  years  at  the  ordinary 
temperature.  Further,  the  possible  presence  of  traces  of  solvent 
must  be  most  carefully  guarded  against,  for  in  the  case  of  certain, 
chemically  isomeric  (tautomeric)  substances  which  transform  into 
one  another  only  in  solution,  the  transformation  may  be  induced 
by  a  trace  of  the  solvent,  and  so  the  one  crystallised  state  will 
apparently  be  transformed  directly  into  the  other.1  At  the  same 
time  it  must  be  remarked  in  this  connection  that,  in  the  case 
of  a  number  of  chemically  isomeric  substances,  observations 
have  been  recorded  which  go  to  show  that  even  in  the  absence 
of  every  trace  of  solvent,  transformation  of  the  one  isomer  into  the 
other  can  take  place.2  On  the  other  hand,  transformation  through 
the  agency  of  a  solvent  can  occur  also  with  polymorphous  modifica- 
tions. In  doubtful  cases,  however,  it  is  possible  to  arrive  at  a 
decision  as  to  whether  isomerism  or  polymorphism  is  present,  from 
a  comparison  of  the  melting  points  of  the  two  crystallised  forms.3 

There  is,  in  addition  to  chemical  isomerism,  another 
phenomenon  which  must  be  distinguished  from  poly- 
morphism, and  which  we  shall  call  polysymmetry.  This 
makes  its  appearance  in  substances  of  so-called  pseudo- 
symmetric  crystalline  form, — that  is  to  say,  substances 
whose  crystal  structure  closely  approximates  to  one  of 
higher  symmetry.  To  this  class  belong,  for  example, 
rhombic,  monoclinic  or  triclinic  crystal  structures  in  which 
the  distances  between  the  neighbouring  similar  material 
particles,  along  three  directions  lying  in  one  plane  and 
intersecting  at  nearly  equal  angles,  are  very  slightly 

1  See  Schaum,  Annalen  aer  Chem.  1898,  300,  223  ;  also  his  inaugural 
dissertation,  Die  Arten  der  homerie,  Marburg,  1897. 

-  See  Wegscheider,  Sitz.  Ber,  d.  Akad.  Wien,  1901,  no,  ii.  918 ; 
Monats.f.  Chem.  22,  919  ;  Journ.  C.  S.  82,  ii.  126. 

:i  See  Wegsch.ider,  loc.  cit.  919  et  seg.  ;  920  et  sej.  ;  also,  more  especi- 
ally, Bruni,  Rend.  Accad.  Lincei,  Rome.  1902  (5)  II,  i.  386  ;  Gazz.  C/iim. 
/t<il.  1903,  33,  i.  100  ;  Journ.  C.  S.  82,  ii.  448. 


6  (HKMICAL  CRYSTALLOGRAPHY 

different.  Such  a  substance  then  exhibits  a  "  pseudo- 
hexagonal  "  crystalline  form,  i.e.,  those  faces  which  together 
complete  an  apparently  hexagonal  form,  though  not 
altogether  equivalent,  are  yet,  in  consequence  of  the 
close  agreement  in  the  arrangement  of  the  particles  in 
them,  so  similarly  favoured  during  the  formation  of  the 
crystal  that  they  regularly  appear  together  and  are  developed 
in  a  similar  manner.  In  this  case  the  crystalline 
form  is  apparently  hexagonal,  and  might  be  imagined  as 
resulting  from  a  really  hexagonal  crystal  by  a  slight 
homogeneous  deformation,  e.g.,  a  rhombic  crystal  by  an 
extension  or  compression  in  the  direction  of  one  of  the 
lateral  axes,  effected  uniformly  on  all  parts  of  the  crystal  ; 
a  monoclinie  one  by  straining  in  an  oblique  direction  lying 
in  a  plane  of  the  hexagonal  prism  ;  finally,  a  triclinic 
pseudo-hexagonal  form  by  a  compression  or  extension  in 
any  general  direction.  Crystal  structures  of  the  kind  here 
described  possess,  as  we  learn  from  physical  crystallography, 
three  kinds  of  positions  in  which  they  are  in  equilibrium 
with  one  another,  as  follows  from  the  fact  that  they  regu- 
larly appear  as  triplet  growths,  twinned  on  the  faces  of  the 
pseudo-hexagonal  prism  (as  so-called  mimetic  forms).  In 
the  usual  case  of  these  mimetic  forms  being  composed  of 
thin  twinned  lamellae,  then,  the  thinner  the  lamellae  (i.e.,  the 
more  frequently  the  three  positions  alternate  with  one 
another  in  the  composition  of  the  whole  structure),  the 
more  will  the  variations  of  the  angles  from  those  of  a 
truly  hexagonal  crystal  become  obliterated.  If,  finally, 
this  alternation  takes  place  in  a  regular  manner,  and  at  such 
minute  distances  that  the  twin  structure  is  no  longer 
recognisable  even  under  the  microscope,  there  results  a 
structure  which  cannot  by  any  of  its  properties  be  dis- 
tinguished from  a  simple  hexagonal  crystal.  In  that  case 
the  substance  appears  in  two  apparently  different  modifica- 
tions, one  hexagonal  and  the  other  rhombic  (or  monoclinie, 
or  triclinic)  pseudo-hexagonal,  with  twin  structure.  Since 

we   have    h-  re   to  do  not   with    a  different   kind  of  crystal 


CRYSTAL  STRUCTURES  7 

structure,  as  in  cases  of  polymorphism,  but  with  a  different 
mode  of  composition  of  the  same  crystal  structure,  we  shall 
distinguish  as  polysymmetric  substances  those  which 
exist  in  modifications  of  this  kind,  possessing  different 
symmetry  ;  the  individual  modifications,  possessing  closely 
agreeing  crystalline  forms  but  differing  in  symmetry,  we 
shall  distinguish  from  the  polymorphous  as  polysymmetric 
modifications. 

The  re-arrangement  into  the  twinned  position,  i.e.,  the 
formation  of  twin  lamellae,  can  be  effected  by  pressure  or 
tension,  as  also  by  alteration  of  the  temperature  of  the 
crystal.  The  state  of  equilibrium  for  that  regular  structure 
in  which  the  crystal  appears  as  quite  simple  and  of  higher 
symmetry,  may  be  a  particularly  stable  one  within  definite 
limits  of  temperature  ;  in  such  a  case,  on  warming  the  poly- 
synthetic  crystal,  not  only  may  the  appearance  of  new  lamellae 
be  observable  at  first,  but  as  the  temperature  limit  is  ap- 
proached, there  may  take  place  gradually  an  apparent  trans- 
formation into  the  more  symmetric  form.  Since  this  is  built 
up  of  the  same  structure  as  the  less  symmetric  form,  but  in 
regular  alternation,  its  properties  must  be  deducible  from 
those  of  the  lower  form  ;  with  polymorphous  modifications 
such  is  not  the  case.  As  regards  the  optical  properties  this 
deduction  is  provided  by  the  theory  which  Mallard 
developed  regarding  the  optical  behaviour  of  crystalline 
packets  ;  a  peculiarly  interesting  case  of  this  is  exhibited 
by  the  enantiormorphous  piling  up  of  pseudo-hexagonal 
lamellae  to  form  an  optically  uniaxial  crystal  exhibiting  right 
or  left  rotation  (quartz). 

In  the  following  paragraphs  a  fuller  description  is  given  of 
a  few  examples  of  polysymmetric  substances. 

Potassium  felspar,  KAlSi:JO8,  is  the  longest-known  example  of 
substances  possessing  this  character.  Its  crystals  sometimes 
exhibit  the  properties  of  quite  simple  monoclinic  individuals  ; 
sometimes  they  are  built  up  of  fine  lamellae  of  a  triclinic  crystal  in 
t\vo  positions,  and  it  is  not  unusual  in  such  cases  to  find  parts  of 
a  crystal  \vhich  even  under  the  highest  magnification  exhibit 


8  CHEMICAL  CRYSTALLOGRAPHY 

no  recognisable  traces  of  lamellation  ;  these  parts,  where  the 
behaviour  is  completely  that  of  a  monoclinic  crystal,  must  con- 
sequently be  looked  upon  as  composed  of  submicroscopic  twin 
lamellae. 

Potassium  sodium  sulphate  (glaserite),  K3Na(SO4)2,  and  the 
analogous  chromate,  K3Na(CrO4)o,  provide  additional  instructive 
examples.  According  to  Gossner's  investigations  they  form 
pseudo-hexagonal  (monoclinic)  crystals,  but  always  aopear  in 
mimetic  aggregates  which  exhibit  a  nearer  approximation  to 
simple  crystals  of  higher  symmetry,  the  higher  the  temperature 
at  which  they  were  crystallised.  Accordingly,  they  also,  on 
warming,  undergo  transformation  into  optically  uniaxial  structures, 
without  exhibiting  any  abrupt  thermal  or  volume  change. 

In  the  above  cases  the  scalar  properties  of  the  two 
modifications  are  the  same,  whilst  in  the  case  of  poly- 
morphous substances  these  properties  (c-g.,  density  and 
specific  heat)  change  when  transformation  takes  place. 
Since,  however,  the  values  for  these  properties  are  depend- 
ent on  the  pressure,  it  is  possible  for  the  difference  between 
two  polymorphous  modifications,  as  regards  one  of  these 
properties,  to  become  zero  at  a  definite  pressure.  Such 
is  the  case  with  the  two  following  substances,  which  at  first 
were  supposed  to  be  polysymmetric  ;  later,  it  was  found 
that  under  high  pressure  the  transformation  is  accompanied 
by  change  of  density,  which  proves  that  they  belong  to  the 
class  of  polymorphous  substances.1 

Sodium  magnesium  uranylacetate,  NaMg(UOo)3(C2H3O2)a,9H._.O, 
according  to  WyroubofPs  investigations,2  crystallises  at  15° 
in  simple  monoclinic  crystals  which,  as  regards  their  angles,  differ 
but  slightly  from  a  combination,  tabular  on  the  basal  plane 
{in(,  consisting  of  two  rhombohedra,  {100}  and  {ni},  with 
a  hexagonal  bipyramid  and  the  prism  of  the  second  kind 
{101}  ;  they  are  therefore  pseudo-trigonal.  At  slightly  higher 
temperatures  twin  sectors  make  their  appearance,  the  twinning 
being  on  the  pseudo  hexagonal  prism  faces  {noj  and  {130}  ;  with 
rising  temperature  the  twin  lamellae  become  finer  and  finer,  and 
suddenly  the  basal  table  appears  singly  refracting  in  parallel 


1  Steinmet/,  /,•//<.  f.  phys.  Chem.  1905,  52,  449  tt  sfj. 

•  />'////.  Sac.  /•'/•.  Mix.   1901,  24,  03  /•'  <••/.  ;  /fit*,  f.  A  ";TV/.  37,   191  ft  sf</. 


CRYSTAL  STRUCTURES  9 

polarised  light,  *>.,  the  monoclinic  crystal  has  undergone  trans- 
formation into  an  optically  uniaxial  trigonal  one.  Steinmetz 
determined  the  transition  temperature  to  be  28°,  and  showed  by 
the  dilatometric  method  that  the  transformation  takes  place 
without  any  change  of  density  ;  the  expansion  curve  is  continuous 
and  almost  rectilinear,  but  with  a  slight  change  of  direction  at 
28°,  which  points  to  the  coefficient  of  thermal  expansion  under- 
going a  slight  alteration  at  that  point.  There  is,  however,  no 
measurable  thermal  effect  accompanying  the  transformation,  as 
shown  by  the  cooling  curve  obtained  by  the  same  observer  ;  under 
a  pressure  of  53  atmospheres,  however,  there  is  a  distinct  effect. 

Isopropylaramonium  chloroplatinate,  (C3H7NH3)oPtCl6,  accord- 
ing to  Ries,1  forms  apparently  rhombic  crystals,  which,  how- 
ever, are  proved  by  optical  investigation  to  consist  entirely 
of  monoclinic  lamellae  assembled  on  the  pinacoid  {100}.  On 
heating  to  32°  the  lamellae  suddenly  disappear,  and  the  crystal 
shows  all  the  properties  of  a  simple  rhombic  crystal,  which, 
on  cooling  below  32°,  again  becomes  transformed  into  the 
pseudo-rhombic  complex  composed  of  twin  lamellae.  With  this 
substance  Steinmetz  found  only  a  slight  decrease  of  density  at 
the  transition  point,  and  the  coefficient  of  expansion  appears  to  be 
not  appreciably  different  above  and  below  the  temperature  of  32° ; 
from  the  cooling  curve  there  also  appears  to  be  no  change  in 
the  specific  heat  on  transformation. 

Amongst  pseudo-symmetric  or  mimetic  crystals,  however, 
there  are  some  which  do  not  undergo  a  transformation 
into  the  apparently  simple  and  more  symmetric  form,  but 
in  which  a  true  (z>.,  a  polymorphous)  transformation  takes 
place,  as  the  following  examples  show  : — 

Calcium  chloraluminate,  Ca.2AlO3Cl,  5H2O,  forms,  according  to 
Friedel,2  apparently  hexagonal  tables,  which,  however,  are  mono- 
clinic  triplets  ;  at  36°  the  boundaries  and  the  slightly  re-entrant 
angles  disappear,  and  the  table  becomes  optically  uniaxial. 
According  to  Steinmetz's  dilatometric  determinations,  there  is  a 
sudden  contraction  in  volume  at  this  point. 

Boracite,  Mg-ClgB^O^,  behaves  similarly ;  its  pseudo-cubic 
crystals  are  built  up  of  numerous  rhombic  lamellae,  and  at  265° 

1  Zeits.f.  Kryst.  ICO2,  36,  329. 

-Bull.  Soc.  Fr.  Min.  1897,  20,  122,  et  seq.  ;  Zeits.f.  K'ryst.  31,  72; 
Journ.  C.  S.  1899,  76,  ii.  366. 


In  CHKMH  AI.  CIIYSTAU.OCKAi'HV 

they  are  suddenly  transformed  into  singly  refracting  truly  cubic 
crystals.  In  this  case  also  there  is  a  distinct  contraction,  and  a 
considerable  absorption  of  heat. 

Potassium  sulphate,  K.jSO4,  forms  rhombic  tables  which  are 
eminently  pseudo-hexagonal,  generally  with  a  triplet  structure 
which  becomes  more  pronounced  on  heating,  so  that  each  crystal 
then  appears  to  be  composed  entirely  of  fine  lamellae  parallel  to 
{no}  and  {130} ;  simple  crystals  also  give  rise  to  twin  lamellae  on 
heating.  Between  600°  and  650°,  according  to  Mallard,  a  sudden 
transformation  takes  place  into  a  simple  optically  uniaxial  crystal, 
whose  double  refraction  is  considerably  stronger  and  of  opposite 
sign  ;  this  excludes  the  assumption  that  it  is  built  up  in  a  regular 
manner  from  sub-microscopic  lamellae  of  the  rhombic  modification. 

Leucite,  KAlSi;>O6,  which  is  pseudo-cubic,  behaves  in  a  quite 
similar  manner,  and  its  transformation,  at  about  560°,  into  a  truly 
cubic  substance  is  apparently  also  a  polymorphous  change. 
Determinations  of  the  thermal  and  volume  relationships  at  the 
transition  point  have  not  been  carried  out  on  this  substance, 
owing  to  the  high  temperature  at  which  the  change  takes  place. 

That,  finally,  one  and  the  same  substance  can  crystallise 
both  in  polysymmetric  and  in  polymorphous  modifications 
is  indicated  by  the  relationships  which  are  observed  in  an 
important  mineral  group— that  of  the  pyroxenes.  The 
compound  RSiOg,  where  R  is  a  bivalent  metal  (Mg,  Mn,  Fe, 
etc.),  exists  (a)  in  monoclinic  crystals,  which  often  con- 
stitute lamellar  twin  structures  of  apparently  rhombic 
I'-nn  ;  also  (b]  in  rhombic  crystals  of  precisely  that  form 
which  would  result  from  the  above-mentioned  twin  lamellae 
becoming  sub-microscopic,  and  lastly  (c)  in  triclinic 
crystals  of  a  distinctly  divergent  form  which  does  not,  by 
twin  formation,  exhibit  gradations  towards  the  two  preceding 
forms.  It  is  therefore  to  be  assumed  that  the  relation 
between  the  first  and  second  forms  is  of  the  nature  of  poly- 
svmriKtry,  whilst  between  these  forms  and  the  last  one  the 
relation  is  that  of  polymorphism,  in  this  case  dimorphism. 

A  further  example  is  supplied  by  the  double  sulphates  KLiSO4 
and  NH4LiSO4.  The  first  of  these  forms  crystals,  belong- 
ing to  the  hexagonal  pyramidal  (lass,  which  rotate  the  plane 
of  polarisation  of  li-ht,  and  \\hosc  structure  may  therefore 


CRYSTAL  STRUCTURES  11 

be  looked  upon  as  a  spiral  polysynthetic  one,  lamellar  on  the 
hexagonal  basal  plane.  The  analogous  ammonium  salt  does 
actually  exist  in  rhombic  crystals  with  eminently  pseudo-hexagonal 
structure  ;  these  frequently  form  triplets  possessing  lamellar  struc- 
ture parallel  to  the  basal  plane,  the  lamellae  often  being  so  thin 
that  the  crystals  appear  almost  uniaxial  and  exhibit  distinct 
rotation  of  the  plane  of  polarisation.  This  rhombic,  or  hexagonal, 
form  of  ammonium  lithium  sulphate  is  not  the  most  stable  one  at 
ordinary  temperatures,  however,  and  is  deposited  only  from  warm 
solutions  ;  from  cold  aqueous  solutions  a  different  (polymorphous) 
modification  is  produced  ;  this  also  forms  rhombic  crystals,  it  is 
true,  but  has  a  totally  different  crystal  structure. 

Though  it  appears,  from  what  precedes,  that  several  cases 
exist  in  which  further  investigation  is  required  to  show 
whether  the  differently  crystallised  modifications  of  the 
substance  are  polysymmetric  or  polymorphous,  the  two 
phenomena  of  polysymmetry  and  polymorphism  are  so 
essentially  distinct  from  one  another  that  they  must  be 
looked  upon  as  depending  on  different  causes.  These 
differences  may  be  summed  up  in  the  following  manner  : — 

The  crystals  of  that  polysymmetric  form  of  a  substance,  in 
which  the  twin  growth  is  no  longer  recognisable,  are  only 
apparently  homogeneous  bodies,  and  they  differ  from  the  simple 
or  the  evidently  twinned  crystals  of  the  form  with  lower 
symmetry  only  as  regards  those  properties  which  are  con- 
ditioned by  the  way  in  which  they  arc  built  up  out  of  the 
latter.  Between  the  two  forms  there  exist  intermediate  stages 
with  continuously  varying  properties,  and  transformation  from 
the  one  form  into  the  other  does  not  take  place  at  a  definite 
temperature. 

Polymorphous  modifications,  on  the  other  hand,  represent 
really  different  states  (phases).  On  the  transition  from  one 
to  the  other  there  takes  place,  in  general,  a  discontinuous 
change  of  all  the  properties,  scalar  as  well  as  vector,  and 
the  transformation  takes  place  at  a  definite  temperature — the 
transition  point  (pressure  being  assumed  constant,  and  leav- 
ing out  of  account  retardations  due  to  overheating  or  over- 
cooling). 


1  L  CHEMICAL  CRYSTALLOGRAPHY 

If  it  is  the  case,  as  was  assumed  in  the  first  instance, 
that  the  difference  between  the  polymorphous  modifications 
of  a  substance  depends  on  a  different  arrangement  of  its 
smallest  material  particles,  the  question  presently  arises  : 
Are  these  smallest  particles,  the  so-called  crystal  mole- 
cules, identical  with  the  chemical  molecules,  or  (as  has 
been  widely  assumed),  are  they  composed  of  a  number  of 
chemical  molecules?  Since  a  direct  determination  of  the 
molecular  weight  is  possible  only  for  substances  in  solution 
or  in  the  gaseous  state,  attempts  have  been  made  to  decide 
this  question  by  employing  an  indirect  method  based  on 
the  theory  of  so-called  solid  solutions.1  The  results  of  these 
attempts,  however,  require  for  their  interpretation  such  mani- 
fold assumptions,  that  this  method  of  determining  molecular 
weights  cannot  be  described  as  free  from  objection.  It  can 
be  shown,  however,  that  the  difficulties  of  the  question 
under  consideration  are  obviated,  and  the  question  itself 
becomes  superfluous,  as  soon  as  we  accept  that  theory  of 
crystal  structure  which  alone  supplies  an  explanation  of 
all  the  manifold  symmetry  observed  and  possible  with 
crystals,  namely,  the  "  Extended  Theory  of  Crystal 
Structure,"  propounded  by  Sohncke  in  the  year  1888.- 
This  states  that : 

A  crystal  consists  of  d  finite  number  of  interpenetrating 
regular  point  sy items  ^  which  all  possess  like  ami  like -directed 
went*.  Each  separate  point  system  is 
•tccupied  by  similar  material  particles,  but  these  may  be 
different  for  the  different  interpenetrating  partial  systems 
<\  Inch  I'irm  the  complex  system? 

The  points  of  such  a  partial  system  may  equally  well  be 
supposed  to  be  occupied  by  similar  atoms,  as  by  molecules 
(Sohncke,  himself,  for  that  matter,  had  this  idea  in  his 

1  Sec  van 't  Hoff,  Lectures  on  Theoretical  ana  Physical  Chemistry,  transla- 
tion by  Lehfeldi,  2,  70. 

2  Xtitt.  /.  h'ryst.  14,  431  ft  stq. 

n  Thai  they  should  be  the  same  is  consequently  not  excluded  on  this 
theory,  which  in  itself  is  purely  mathemntinl  ;  u<  h  a  c:is«-  is  improl.al.lc, 
however,  on  mechanical  grounds. 


CRYSTAL  STRUCTURES  13 

mind  (loc.  tr//.),  but  did  not  pursue  it  further)  ;  for  atoms, 
like  molecules,  are  possessed  of  specialised  directions,  as 
shown  by  their  valency,  by  stereo-isomerism  and  other 
chemical  relations,  apart  altogether  from  their  possible 
compound  nature  and  the  localised  electric  charges  (or  the 
electric  currents  circulating  about  them  in  a  definite  manner) 
in  which  probably  are  to  be  sought  the  origin  of  those 
forces  whose  equilibrium  determines  the  crystal  structure. 
On  that  supposition  all  the  atoms  in  any  such  partial 
system  would  be  orientated  parallel  to  one  another  only  in 
the  special  case  of  their  forming  a  simple  space  lattice  ;  in 
general  the  partial  system  will  be  formed  by  the  inter- 
penetration  of  several  space  lattices  which  differ  in  the 
orientation  of  the  atoms  composing  them. 

If,  for  example,  three  regular  point  systems  of  this  kind, 
possessing  similar  coincidence  movements  and  consisting 
one  of  sulphur  atoms,  another  of  twice  as  many  potassium 
atoms,  and  the  third  of  four  times  as  -many  oxygen  atoms, 
are  fitted  the  one  within  the  other  in  such  a  way  that 
equilibrium  is  maintained,  there  results  a  crystal  structure 
with  the  properties  and  chemical  composition  of  crystallised 
potassium  sulphate.  This  structure  completely  fulfils  the 
condition  of  u  regularity,"  for  within  it  there  exist,  at 
equal  but  immeasurably  small  distances,  homologous  posi- 
tions (those  of  the  similarly  orientated  atoms  of  each  of 
the  space  lattices),  ?>.,  "points,  about  each  of  which  the 
mass  distribution  parallel  to  any  chosen  direction  in  the 
crystal  is  the  same  as  about  any  other." 

It  is  evident,  however,  that  in  such  a  structure  "  mole- 
cules," in  the  sense  in  which  we  speak  of  gaseous  molecules, 
are  altogether  wanting,  and  it  is  a  matter  of  choice  what  is 
to  be  called  the  unit  of  crystal  structure  or  the 
crystal  molecule ;  for,  just  as  it  is  quite  arbitrary  which 
mass-points  of  a  regular  point  system  may  be  supposed 
to  constitute  a  closer  group,  so  there  are  various  ways  in 
which,  with  equal  right,  adjacent  potassium,  sulphur,  and 
oxygen  atoms  may  be  supposed  to  constitute  a  K2SO4 


1  i  CHEMICAL  CRYSTALLOGRAPHY 

group,  or  (with  twice  the  number)  a  K4S2O8  group.  The 
K0SO4  molecules  exist  in  the  structure  only  in  so  far  that, 
when  the  structure  is  demolished,  by  the  fusion,  dissolution, 
or  vaporisation  of  the  crystal,  it  is  possible  for  the  chemical 
molecules  (or,  in  some  circumstances,  multiples  of  them), 
to  result  directly,  in  consequence  of  the  interpenetration 
of  the  regular  point  systems  composed  of  the  different 
atoms. 

It  is  at  once  evident  that  polymorphous  modifications 
must  yield  identical  liquids,  solutions,  or  vapours,  if  the 
relative  positions  of  the  atoms  contained  in  their  structure 
is  similar,  and  only  the  point  systems  (that  is  to  say,  the 
space  lattices  composing  them,  which  define  the  crystal 
structure),  and  the  coincidence  operations  characteristic 
of  them,  are  different  ;  for  the  point  systems  and  space 
lattices  are  destroyed  on  the  passage  into  the  amorphous 
(or  the  dissolved)  state.  With  chemically  isomeric  sub- 
stances, in  that  volume  which  contains  the  neighbouring 
atoms  corresponding  to  a  chemical  molecule,  the  relative 
position  of  the  atoms  is  quite  different  ;  naturally,  in  con- 
sequence of  this,  the  point  systems  built  up  from  them 
are  also  different,  and  so  is  the  resultant  space  lattice 
characteristic  of  the  whole  structure. 

In  the  case  of  a  crystallised  element  the  theory  is 
reduced  to  that  of  a  single  regular  point  system,  composed 
of  similar  interpenetrating  space  lattices  in  such  a  way  that 
the  atoms  form  closer  groups  (Sohncke's  "  ;/-Punktner "). 
Since  this  is  possible  in  various  ways,  and  in  addition  the 
space  lattices  themselves  can  be  different,  owing  to  poly- 
morphism, there  is  the  possibility  of  a  very  great 
multiplicity  of  modifications  in  the  case  of  the  elements. 
Those  amongst  them  in  which  these  closer  groups  of  the 
crystal  structure  differ  as  regards  number  or  arrangement 
of  the  atoms  composing  them,  break  up,  on  passing  into  the 
amorphous  or  the  dissolved  state,  into  molecules  which 
behave  as  those  of  chemically  isomeric  or  polymeric  sub- 
stances. This  explains  the  circumstance  that  certain 


CRYSTAL   STRUCTURES  15 

t(  allotropic   modifications "  of  an    element  may  not  yield 
identical  solutions  or  vapours. 

Like  polymorphism,  the  relations  between  crystal  form 
and  chemical  constitution,1  to  be  discussed  later,  are  in 
accord  with  the  above  view  as  to  the  structure  of  crystallised 
substances,  which,  as  already  mentioned,  is  also  capable  of 
explaining  all  the  phenomena  of  symmetry  observed  in 
connection  with  crystals. 

1  In  addition  to  the  relationships  designated  by  the  names  of  morphotropy, 
isomorphism,  etc.,  which  will  be  treated  in  subsequent  sections,  there  is  one 
matter  which  may  be  referred  to  at  this  point.  According  to  the  theory 
here  adopted,  the  crystal  structure  of  those  substances  whose  molecules 
contain  three  or  six  similar  atoms,  such  as  : — A10O3  ;  NaNO3 ;  CaCOo  ; 
MgSiF6,6H20;  Na3Fe(SO4),,3H2O;  C6H4(OH>, ;  CcH3(COO.CoH,)3,etc., 
must  contain  a  point  system  built  up  of  three-point  or  six-point  groups  j 
now,  since  the  symmetry  of  this  system  must  exercise  an  influence  on  the 
symmetry  of  the  combined  system,  the  frequent  occurrence  of  trigonal 
or  hexagonal  crystal  forms  with  such  substances  becomes  explicable. 


POLYMORPHISM 

ACCORDING  to  the  preceding  considerations,  the  idea  of 
polymorphism  is  to  be  confined  to  those  homogeneous, 
physically  different  states  of  a  substance,  in  which  the 
difference  depends  on  a  difference  in  their  crystal  structure. 
Given  that  on  the  transformation  of  one  polymorphous  modi- 
fication into  the  other  there  occurs  a  discontinuous  change  of 
properties,  the  transition  point  presents  certain  analogies 
with  the  melting  point  and  freezing  point.  As  a  matter  of 
fact,  there  is  a  thermal  effect  on  changing  from  a  state  A, 
more  stable  at  low  temperatures,  into  a  state  B,  more 
stable  at  higher  temperatures,  and  as  a  rule  B  possesses 
a  higher  specific  heat  and  a  lower  density  than  A.  At 
the  transition  point,  A  and  B  are  in  equilibrium,  and  this 
point  exhibits  the  same  dependence  on  pressure  which  is 
observed  in  the  case  of  the  melting  point,  i.e.,  if  the  change 
from  A  into  B  is  accompanied  by  an  increase  of  volume, 
then  the  transition  temperature  rises  with  increasing 
pressure,  in  accordance  with  the  same  law  which  applies 
to  the  melting  point. 

Transgression  of  the  transition  point,  in  either  direction, 
may  be  unaccompanied  by  transformation,  but,  like  the 
over-cooling  of  a  liquid  below  its  freezing  point,  this  is  pos- 
sible only  if  no  trace  of  the  new  modification  is  present. 
If  such  transgression  has  taken  place,  then  the  substance 
exists  in  a  state  which,  as  proposed  by  Ostwald,1  is 
designated  as  metastable,  because,  whilst  it  corresponds  to 

1  Zeits./.phys.  Chtm.  1897,  22,  3°2  ;  Journ.  C.  S.  72,  ii.  308. 
10 


POLYMORPHISM  17 

a  stable  equilibrium,  it  nevertheless,  merely  on  contact  with 
the  other  modification  which  is  now  the  most  stable  one,  is 
terminated  by  transformation  accompanied  by  the  correspond- 
ing thermal  effect.1  On  the  other  hand,  that  condition  in 
which  the  transformation  commences  spontaneously,  even 
without  previous  contact  with  the  second  modification, 
must  be  designated  as  essentially  labile.  In  both  cases 
it  is  possible  for  the  transformation  to  take  place  very 
rapidly,  but  it  can  also  be  a  very  slow  one,  depending  on 
the  rigidity  of  the  system.  Whilst,  in  the  neighbour- 
hood of  the  transition  point,  the  tendency  towards  trans- 
formation (and  consequently  the  rate  of  transformation) 
naturally  increases  with  the  distance  from  that  point  of 
equilibrium,  the  rigidity  of  the  structure,  which  resists 
that  tendency,  is  continually  augmented  by  increased 
over-cooiing,  and  the  result  may  be  that  below  a 
certain  temperature  the  rate  of  transformation  is  zero  ; 
under  these  circumstances  both  modifications  exist  side 
by  side,  apparently  quite  indifferent.  Behaviour  of  this 
kind  has  been  proved  by  Gernez  in  the  case  of  sulphur, 
and  also  by  Schaum2  in  the  case  of  hexachloroketo- 
dihydrobenzene.  This  explains  why  aragonite,  which  is 
the  metastable  form  of  calcium  carbonate  at  ordinary  tem- 
peratures, can  exist  unchanged  in  contact  with  calcite, 
the  stable  form,  and  changes  into  the  latter  only  at  a 
somewhat  high  temperature,  in  the  neighbourhood  of  the 
transition  point. 

We  shall  now  consider  in  a  somewhat  more  detailed 
manner  several  examples  of  substances  whose  polymorphous 
modifications  have  been  investigated,  as  regards  their 
relations  to  one  another,  with  some  accuracy. 

Sulphur  can  exist  in  a  series  of  crystallised  modifications,  two 
of  which — the  rhombic  one  usually  obtained  by  deposition  from 

1  From  the  nature  of  the  difference  between  polymorphous  and  poly- 
symmetric  substances  it  follows  that  in  the  latter  a  metastable  condition 
is  not  possible. 

-  Die  Artcn  acr  homer  ic. 

\\ 


18  CHEMICAL  CUYSTALLOGftAPHY 

solution,  and  the  monoclinic  one  which  crystallises  from  the 
fused  substance— belong  to  the  longest  known  cases  of  poly- 
morphism (discovered  by  Mitscherlich !)  and  have  been  the 
most  thoroughly  studied.  The  rhombic  modification,  which 
possesses  the  higher  density  and  the  lower  specific  heat  is 
stable  up  to  about  96°,  when  it  becomes  transformed  into  the 
monoclinic  form,  with  absorption  of  heat  (heat  is  evolved  in  the 
reverse  process).  The  transition  temperature  can  be  easily 
exceeded,  however,  without  transformation  taking  place,  and  by 
cautiously  raising  the  temperature  (with  most  careful  exclusion 
of  any  trace  of  monoclinic  sulphur)  it  is  even  possible  to 
bring  the  now  metastable  rhombic  sulphur  into  a  state  of 
fusion — which  takes  place  at  113-5° — without  it  having  undergone 
transformation  into  the  monoclinic  modification  ;  the  latter,  once  it 
has  been  formed,  melts  only  at  1 19-5°  (according  to  the  observations 
of  Brodie,  Gernez,  and  Muthmann).  Conversely,  the  monoclinic 
sulphur  crystallised  from  the  fused  substance,  provided  all  contact 
with  the  rhombic  form  is  avoided,  can  be  over-cooled  very  far, 
even  to  the  ordinary  temperature,  without  transformation.  In 
that  case,  however,  a  spontaneous  transformation  soon  takes 
place  (so  that  here  already  we  have  to  deal  with  a  labile  con- 
dition), and  once  started  it  proceeds  rapidly.  A  transgression 
of  the  transition  temperature  never  takes  place  if  the  other 
modification  is  present ;  it  is  therefore  possible  to  determine  the 
temperature  of  equilibrium  by  examining,  with  the  help  of 
Lehmann's  crystallisation  microscope  (page  4),  a  preparation  in 
which  the  two  modifications  are  in  contact  with  each  other,  and 
determining  the  temperature  at  which  no  shifting  of  the  boundary 
between  them  takes  place,  to  the  one  side  or  the  other.  The 
determination  by  means  of  the  dilatometer  is  more  accurate, 
since  on  the  transformation  of  rhombic  sulphur  (density  2-07) 
into  monoclinic  (density  1-96),  a  considerable  increase  in  volume 
takes  place,  and  on  the  reverse  transformation  there  is  a  cor- 
responding contraction.  In  this  way  Reicher2  determined  the 
transition  temperature  to  be  95-6'',  and  showed  that  it  rises  with 
increasing  pressure,  the  increment  for  one  atmosphere  being  0-05°. 
\Vhcn  molten  sulphur  in  a  perfectly  clean  vessel  is  very 
carefully  cooled  below  the  temperature  of  solidification,  it  is 

1  Abhandl.    d.    Akad.    Berlin,     1822.     Gtsammelfe    Schrifien    rent    E. 

:trlicht  Berlin,  1896,  lyottseq. 
'*  /tits./.  A'mA  1884,  8,  593  el  ss>/. 


POLYMORPHISM  19 

possible  to  induce,  in  the  over-cooled  liquid,  the  crystallisation 
of  the  one  or  the  other  modification  at  will  by  contact  with  a 
crystal  of  that  modification  ;  under  otherwise  similar  conditions, 
however,  the  solidification  of  the  liquid  to  form  rhombic  crystals  is 
propagated  25-100  times  faster  than  the  monoclinic  crystallisation.1 
Even  below  the  transition  temperature  the  latter  process  can  be 
induced  in  the  over-cooled  liquid  by  inoculation  with  a  mono- 
clinic  crystal.  The  transformation  of  monoclinic  solidified  sulphur 
into  the  rhombic  modification,  on  contact  with  the  latter,  naturally 
proceeds  but  slowly  in  the  neighbourhood  of  the  transition  point ; 
the  rate  of  transformation  at  first  increases,  the  lower  the  tem- 
perature at  which  the  experiment  is  conducted,  but  it  reaches  a 
maximum  at  about  50°  and  thereafter  diminishes  again,  so  that 
at  -  23"  it  is  almost  zero.2 

Below  the  transition  point,  the  solubility  of  monoclinic  sulphur 
is  greater  than  that  of  the  rhombic  modification,  and  it  has  been 
shown  that,  with  chloroform,  benzene,  and  ether,  the  ratio  of 
the  solubilities  of  the  two  modifications  exhibits  that  relation- 
ship to  the  heat  of  transformation  which  is  required  by  theory.3 

Spring4  subjected  freshly  prepared  monoclinic  sulphur  to  a 
pressure  of  5000  atmospheres  at  13°;  the  mass  was  found  to  have 
become  distinctly  harder,  and  possessed  the  density  and  the 
melting  point  of  the  rhombic  modification. 

Mercuric  iodide,  Hglo,  represents  a  second  example  of 
dimorphism,  which  also  was  first  demonstrated  by  Mitscherlich. 
P^rom  solutions  it  is  obtained  in  red  tetragonal  crystals,  but  from 
the  molten  mass,  or  by  sublimation,  in  yellow  rhombic  crystals. 
On  cooling,  the  latter  transform,  with  evolution  of  heat,  into 
aggregates  of  the  red  modification,  and  these  can  be  reconverted 
into  the  yellow  modification  by  careful  heating.  By  Schwarz,5  to 
whom  we  owe  a  very  careful  investigation  of  these  substances, 
the  transition  point  was  determined  to  be  126-3°.  This  can  be 

1  Gernez,  Compt.  rend.  1883,  97,  1477  ;    Zeits.  f.  A'lysf.  n,  102  ;  Jouni. 
C.  S.  46,  553- 
-  Gernez,  Ann.  d.  chim.  etphys.  1886,  [6]  7,  233  ;  Zeits.  f.  Kryst.  13,  427. 

3  J.  Meyer,  Zeits.  f.  anorg.  Cfum.  1902,  33,  140  ;  Journ.  C.  S.  84,  ii.  137. 

4  Bull.  A  cad.  Belg.  1 880,  [2]  49,  351. 

5  W.  Schwarz,  Prize  Essay,  University  of  Gottingen,  1892:    "  Beitrage 
zur   Kenntniss  der  umkehrbaren   Umwandlungen  polymorphen   Korper," 
(Zeits.  f.  Kryst.  25,  613).     This  work  also  contains  a  complete  summary 
of  the  results  of  earlier  investigations. 


•V>  CHEMICAL  CRYSTALLOGRAPHY 

easily  transgressed,  for  generally  it  is  only  at  about  129  that  ;i 
partial  transformation  begins  to  be  apparent,  whilst  conversely, 
when  no  trace  of  the  red  modification  is  present,  yellow  crystals 
can  be  cooled  even  as  far  as  the  ordinary  temperature  ;  but  then 
transformation  may  be  induced  by  contact  with  any  solid  body, 
as  for  example  by  scratching.  On  the  transformation  of  the  red 
modification  into  the  yellow  there  is  a  sudden  and  considerable 
expansion  (Rodwell) ;  and,  in  accordance  with  the  accompanying 
thermal  effect,  the  specific  heat  of  the  yellow  modification  is  less 
than  that  of  the  red  (Schwarz). 

///  vacua,  mercuric  iodide  vaporises  to  a  considerable  extent 
even  at  fairly  low  temperatures,  so  that  the  gaseous  substance 
can  be  obtained  both  from  the  red  (below  126°)  and  from  the 
yellow  (126°)  modifications.  If  a  cooler  solid  body  is  introduced 
into  this  vapour,  the  crystals  which  deposit  on  it  are  always  the 
yellow  modification,  provided  it  possessed  a  perfectly  clean  surface  ; 
should  this  have  been  previously  lightly  rubbed  at  one  spot  with 
crystals  of  the  red  modification,  at  another  with  those  of  the  yellow, 
then  red  crystals  deposit  on  the  former  and  yellow  ones  on  the 
latter.1  From  solutions,  also,  both  red  and  yellow  modifications 
can  be  obtained,  the  latter  even  at  ordinary  temperatures  by 
rapid  separation,  e.g.y  from  supersaturated  solutions,  or  on 
formation  by  double  decomposition.2  This  is  in  accordance 
with  "Ostwald's  rule,"  to  be  mentioned  later. 

Hexachlorethane,  CjCl,},  forms  rhombic  crystals  at  ordinary  tem- 
peratures, but  on  warming  is  transformed  into  a  triclinic,  and  at  a 
still  higher  temperature,  into  a  cubic  modification/'  Schwarz  (loc. 

45)  determined  the  two  transition  temperatures,  and  found  the 
first  to  be,  on  warming,  45-46°,  on  cooling,  43°  ;  the  second  trans- 
formation takes  place  without  any  transgression  of  the  transition 
point,  either  on  wanning  or  on  cooling,  exactly  at  71-1°.  According 
to  experiments  by  Steinmetz,  both  transformations  (with  rising 
temperature)  are  accompanied  by  considerable  expansion,  so  that 
the  rhombic  modification  (density  2-091,  according  to  Gossner  l) 
is  the  densest,  and  the  cubic  one  the  least  dense. 

1  Gernez,  Compt.  rend.  1899,  128,  I$l6  ;  Ann.  d.  chim.  t.  d.  phys.  1900, 
[7]  20,  384  t*  "?•  ;  Zeits.f.  Kryst.  34,  312,  Journ.  C.  S.  76,  ii.  597. 

-  Lchm.-inn,  Molekularphysik^  I,  631  ;  Gernez,  ConiH.  rsn<l.  1903,  136, 
1322;  /ou» ...  C  84,  ii.  481. 

"hminn.  /.,•!'<./.  AVn/.  iSSr.  6,  584. 
Zeih.J.  K,yM.  1903,38,  iji. 


POLYMORPHISM  21 

Ammonium  nitrate,  NH4NO,,  according  to  Lehmann's  investi- 
gations,1 between  the  ordinary  temperature  and  its  melting  point 
passes  through  the  limits  of  stability  of  no  less  than  four  modi- 
fications ;  consequently,  it  is  "  tetramorphous."  The  dry  salt 
melts  at  168°,  the  moist  salt  somewhat  lower,  since  it  dissolves 
in  a  very  small  quantity  of  water ;  in  both  cases  it  solidifies 
to  optically  isotropic  crystal  skeletons.  At  125-6°  the  mass 
suddenly  becomes  doubly  refracting,  and  in  the  case  of  a 
solution  optically  uniaxial  crystals  are  formed  (rhombohedra). 
If  the  solution  cools  still  further,  then,  at  82-8°  there  are  produced, 
from  the  growths  of  the  former  modification,  needle-shaped 
rhombic  crystals,  orientated  in  definite  directions  with  regard  to 
the  preceding  growths.  Finally,  at  32-4°,  these  rhombic  crystals 
become  transformed  into  a  fourth  modification  which  is  also 
rhombic ;  this  is  the  one  which  is  obtained  in  large  crystals 
from  aqueous  solutions  at  ordinary  temperatures.  If  this  last 
modification  is  heated  it  becomes  successively  transformed  into 
the  three  other  modifications  at  the  appropriate  temperatures. 
Bellati  and  Romanese  determined  the  changes  in  the  densities 
and  in  the  specific  heats  at  the  transition  temperatures,2  and 
Schwarz3  gave  a  more  exact  determination  of  the  transition 
temperatures  ;  his  values  have  been  inserted  above  in  place  of 
those  originally  found  by  Lehmann.  Bellati  and  Romanese 
found  for  the  mean  specific  heats 

From    o°-  32°  (first  rhombic  modification)     .          .          .         0-407 
„      32°-  83°  (second     „  „  )     .  0-335 

„      83°-! 24°  (trigonal  „  )     .  0-426 

and  from  their  determinations  Schwarz  calculated  the  densities 
and  their  reciprocal  values — the  specific  volumes — of  the  three 
modifications,  as  follows  : — 

First  rhombic  modification  at  32°     ^=1.6560     Sp.  Vol.  =  0-6039 

Second  fat  32  1-6°21  °'6241 

\at83  1.5875  0-6299 

Trigonal  ,.  at  83  1-6093  0-6214 

On  the  transformation  of  the  last  of  these  modifications  into 

1  Zeits.f.  Kryst.  1877,  I,  106  ;  MolekntQrphysik,  I,   155. 
-  Atti.  1st.  Sc.  Lett.,  etc.,  Venice,  1886,  [6]  4,  1395  ;  Zeits.f.  A'ryst.  14, 
78  ;  Journ.  C.  S.  54,  1 06. 

3  Beilriige  znr  Kenntniss  der  polymorphen  Korper. 


_'L>  CHKMK  AL  CRYSTALLOGRAPHY 

the  cubic  one  there  is  again  a  considerable  increase  in  volume. 
In  this  case,  therefore,  the  first  and  third  transformations  take 
place  with  increase  of  volume,  the  second  with  contraction  ;  the 
temperature  at  which  this  second  transformation  takes  place 
must  therefore,  like  the  melting  point  of  ice,  fall  with  increase 
of  pressure,  in  contrast  to  the  two  other  transition  temperatures, 
which  must  follow  the  common  rule.1  The  solubility  of  the 
first  rhombic  modification  increases  regularly  with  rising  tempera- 
ture up  to  the  transition  point ;  here  there  is  a  diminution  in 
the  solubility,  followed  again  by  a  steady  increase ;  on  the 
other  hand  the  transformation  into  the  trigonal  modification 
is  coincident  with  a  sudden  rise  in  the  solubility,  which  then 
again  increases  in  a  regular  manner  with  rising  temperature 
(Schwarz,  loc.  cif.}. 

As  is  evident  from  the  preceding  examples,  it  is  chiefly 
the  temperature  which  determines  the  formation  of  poly- 
morphous modifications  ;  consequently,  at  different  tem- 
peratures the  one  or  the  other  form  may  be  obtained  even 
from  the  same  solution.  Nevertheless,  the  case  of  mercuric 
iodide  shows  that  other  circumstances  as  well  exercise 
an  influence  in  determining  the  production  of  the  one  or 
the  other  modification.  Thus,  the  salt  in  whose  case 
Mitscherlich  for  the  first  time  (1821)  demonstrated  the 
phenomenon  of  dimorphism,  namely,  sodium  dihydrogen 
phosphate,  NaH2PO4,H9O,  crystallises,  on  cooling  a  warm 
aqueous  solution,  in  the  usual  rhombic  form,  whilst  at 
lower  temperatures  and  under  certain  circumstances  (not 
exactly  known)  a  second  and  very  unstable  rhombic  form 
is  obtained.  A  case  which  in  this  respect  has  been  sub- 
jected to  much  closer  investigation,  especially  through 
the  thorough  researches  of  Vater,2  is  that  of  the  separation 
of  calcium  carbonate  from  carbonic  acid  solution.  Accord- 

1  Tammann,  R'rystallisitrtn  und  Schmelzni,  Leipzig,  1903,  300. 

2  H.    Vater,    "  Ueber    den    Einfluss    der    Ltisungs-genossen    auf    die 
{Crystallisation    des     Calciumcarbonates,"     Zeits.    f.     Kryst.     1893,     21, 
433-490;    1894,   22,    209-228;    1895,    24,    366-404;    1897,    27,   477-504; 

1899,  £>,  295-298,  485-508,  31,  538-578;  1901,  35,  149-178, 


POLYMORPHISM  23 

ing  to  him  it  is  always  the  stable1  trigonal  form,  calcite, 
which  crystallises  out  from  pure  aqueous  solutions  at  tem- 
peratures below  30°,  whilst  from  hot  solutions,  especially 
on  rapid  cooling,  the  metastable  rhombic  modification, 
aragonite,  separates.  But  if  there  are  in  the  solution 
small  quantities  of  strontium  carbonate  or  lead  carbonate, 
then  aragonite  may  separate  even  at  low  temperatures.2 
That  even  with  pure  solutions  the  production  of  a 
different  modification  of  a  substance  may  be  con- 
ditioned by  supersaturation,  as  in  the  case  of  mercuric 
iodide,  is  further  shown  by  the  researches  of  Lecoq  de 
Boisbaudran  3  on  the  vitriols  ;  from  supersaturated  solutions 
of  these  salts  there  separated  in  the  first  place,  as  a  rule, 
that  form  which  at  the  temperature  of  the  experiment 
was  the  less  stable.  This  is  always  the  case  when  the 
supersaturated  solution  is  brought  into  contact  with  a 
crystal  of  the  metastable  modification,  whilst  inoculation 
of  it  with  the  stable  form  of  course  brings  about  the 
crystallisation  of  the  latter.  Similarly,  the  formation  of 
the  one  modification  or  the  other  from  the  fused  mass  may 
be  brought  about  at  will  by  contact  with  the  appropriate 
crystallised  substance,  but  it  goes  without  saying  that  it 
is  not  possible  to  bring  about  the  separation  of  a  very 
slightly  stable  (labile  or  metastable)  modification  if  there 
are  present  the  merest  traces  of  the  stable  modification. 
An  excellent  example  of  this  is  supplied  by  benzophenone, 
CO(C6H5)2,  which  possesses,  in  addition  to  the  stable 
rhombic  form  (m.p.  48-49°)  commonly  produced,  a  meta- 
stable (probably  monoclinic)  modification  which  melts  at 

1  That  calcite  is  at  ordinary  temperatures  the  stable  modification  of 
calcium  carbonate,  and  aragonite  the  metastable  one,  is  shown  by  the 
greater  solubility  of  the  latter  (Foote,  Zeits.  f.  phys.  Chem.  1900.  33,  740; 
^Zeits.  f.  Kryst.  36,  294  ;  Journ.  C.  S.  78,  ii.  541). 

-  Credner,  Journ.  f.  prakt.  Chem.  1870  [2]  2,  292  ;  Journ.  C.  S.  24, 
670. 

"  Ann.  d.  chim.  e.  d.  phys.  1866,  [4]  9,  173  ;  1869,  [4]  18,  246.  See 
also  J.  M.  Thomson,  Journ,  C.  S.  1879,  35,  196. 


•_'!  CHEMICAL  CRYSTALLOGRAPHY 

This  form  was  first  obtained  accidentally  by  Zincke,1 
while  preparing  the  substance,  and  he  found  he  could 
reproduce  it  from  the  fused  material  by  inoculation  with 
a  crystal  fragment.  Closer  investigations  into  the  circum- 
stances under  which  it  is  possible  to  obtain  the  second 
modification  from  the  fused  mass,  instead  of  the 
stable  one,  have  been  carried  out  by  Schaum2  and  by 
Schoenbeck.8 

The  spontaneous  production  of  a  less  stable  form  of 
this  kind  in  a  molten  mass  has  its  analogue  in  the 
previously  mentioned  separation  of  such  a  modification 
from  a  supersaturated  solution  (although  the  less  stable 
form  is  more  soluble,  and  consequently  less  removed  from 
its  point  of  saturation,  than  is  the  more  stable  form,  which 
on  this  ground  should  first  make  its  appearance)  ;  a  further 
analogy  is  supplied  by  the  phenomena  associated  with 
certain  chemical  reactions.  Ostwald 4  has  summed  up 
these  results  in  the  rule  "  that  on  leaving  any  state,  and 
passing  into  a  more  stable  one,  that  which  is  selected  is  not 
the  most  stable  one  under  the  existing  conditions,  but  the 
nearest"  (i.e.,  that  which  can  be  reached  with  the  minimum 
loss  of  free  energy).  Ostwald  illustrates  this  rule  by  means 
of  the  curves  which  represent,  for  the  different  states,  the 
dependence  of  the  vapour  pressure  (/),  or  of  the  solubility, 
on  the  temperature  (7*)  ;  somewhere  or  other  these  curves 
must  intersect  in  pairs.  Suppose,  for  example,  that  / 
(Fig.  i)  represents  the  vapour-pressure  curve  for  rhombic 
sulphur,  77  that  for  the  monoclinic  form,  and  S  that  for 
the  fused  substance  ;  then  s}  and  s2  are  the  melting  points  of 
the  two  crystallised  modifications,  and  //  is  the  transition 
point.  Diffused  sulphur  is  over-cooled,  we  pass  along  the 
curve  5  from  right  to  left  and  arrive,  after  cutting  the 

1  Ber.  d.  d.  chem.  Ges.  1871,  4,  576  ;  Journ.  C.  S.  24,  832. 

7eilt.  f.  phys.  Cktm.  1898,  25,  722  el  se</.  :  frtr*.  C.  S.  74,  jj.  369. 
3  fteitragt  zur  AV*///«m  drr  polymorphfn  A 

"•»i.  1*07.  22,  306  J  fount.  C.  S.  72,  ii.  30*, 


POLYMORPHISM  :_>.~> 

curves  //  and  /in  turn,  first  in  the  region  of  the  ineta- 
stable  condition  and  then  in  that  of  the  labile  one.  On 
reaching  some  point  x  in  this  region,  a  solid  form  must 
appear  spontaneously;  this, 
according  to  the  above  rule, 
will  not  be  the  form  posses- 
sing the  curve  7,  although  it 
is  the  most  stable  at  this  tem- 
perature, but  the  form  //will 
result,  because  it  is  the  most 
adjacent.  If  //  is  then  in  the 
metastable  region  as  regards  /, 
there  the  matter  will  rest,  and 

no  further  transformation  will  take  place  unless  the  product 
comes  in  contact  with  some  of  form  /.  At  the  same  time 
there  is  the  possibility  that  //  may  be  in  the  labile 
region  as  regards  / ;  in  that  case  a  further  spontaneous 
transformation  will  set  in,  and  finally  the  most  stable  form  / 
will  be  reached." 

Fig.  i  represents  the  case  as  it  exists  with  sulphur  and 
many  other  dimorphous  substances.  Below  the  trans- 
formation temperature  //  the  metastable  modification  // 
possesses  the  greater  solubility,  and  likewise,  should  it  be 
volatile,  the  higher  vapour  pressure,  /  ;  at  the  point  u  the 
value  of  /  is  the  same  for  both  modifications  /  and  //,  so 
that  the  two  are  here  in  equilibrium  ;  beyond  u  the  modi- 
fication /,  stable  at  lower  temperatures,  becomes  the 
metastable  form  with  higher  vapour  pressure,  while  the 
previously  metastable  form  //  is  now  the  stable  one  with 
the  lower  value  for  /,  consequently  the  melting  point  sv 
i.e.  the  temperature  of  equilibrium  between  modification  / 
and  the  fused  substance,  is  lower  than  s9j  the  melting 
point  of  the  second  modification  ;  thus,  for  sulphur,  sl  is 
113-5°,  and  -So  is  119-5°  (see  PaSe  J8). 

The  case  represented  in  Fig.  2  is  also  conceivable,  how- 
ever, in  which  the  fusion  curve,  5,  for  the  substance 
lies  below  the  intersection  of  the  curves  /and  //.  Under 


CHEMICAL  CRYSTALLOGRAPHY 

these  circumstances  the  stable  modification  /will  melt  at  sl} 
without  transformation  being  possible  ;  the  metastable  form 
//,  on  the  other  hand,  will  melt  at  a  lower  temperature 

j2,  assuming  that  transforma- 
tion has  not  previously  been 
induced  by  contact  with  /. 
Substances  of  this  kind  will 
therefore  possess  two  crys- 
tallised modifications,  one  of 
which  is  stable  at  all  tem- 
peratures below  its  melting 
—  --^  point  and  never  exhibits 

transformation  into  the  other, 

whilst  the  second  modification  has  a  lower  melting  point 
and  is  metastable  at  all  temperatures  below  that.  Benzo- 
phenone,  mentioned  on  page  23,  is  such  a  substance  ;  for 
it,  consequently,  transformation  is  not  a  reversible  process, 
as  it  is  for  sulphur,  etc.,  but  can  take  place  only  in  one  sense, 
and  at  any  temperature.  Lehmann,  who,  by  his  researches 
with  the  crystallisation  microscope  (page  4),  proved  the 
existence  of  a  considerable  number  of  substances  behaving 
in  this  way,  called  those  of  the  first  kind  enantiotropic 
and  those  of  the  second  kind  monotropic ;  but  sub- 
sequently he  advanced  the  conjecture1  that  the  two  are 
not  essentially  different,  since  the  transition  points  and 
melting  points  are  dependent  on  the  pressure,  and  there- 
fore it  would  probably  be  possible,  by  applying  sufficient 
pressure  to  a  monotropic  substance,  to  bring  the  transition 
point  below  the  melting  point,  whereby  the  substance 
would  change  into  an  enantiotropic  one. 

According  to  the  preceding  considerations,  which 
were  propounded  simultaneously  by  Ostwald2  and  by 
Schaum,8  the  difference  between  the  two  kinds  of  poly- 
morphous substances  does  consist  merely  in  the  posi- 

1  MoUkularphysik,  I,  194. 

2  Zeits.  /.  phys.  Chtm.  1897,  22,  312- 

:fn  dfr  Isomerif,  page  24. 


POLYMORPHISM  27 

tion  of  the  transition  point  relatively  to  the  fusion 
curve  ;  and,  since  increase  of  pressure  shifts  the  vapour- 
pressure  curves  away  from  the  T-axis,  it  depends  on  the 
difference  in  the  displacements  of  the  various  curves 
whether  the  transition-point  u  and  the  vapour-pressure 
curve  S  of  the  fused  substance  approach  one  another,  or 
recede,  with  increasing  pressure.  There  is  therefore  the 
possibility  of  one  and  the  same  substance  appearing  to  be 
monotropic  or  enantiotropic,  according  to  the  pressure. 

The  displacement  of  the  transition  point  and  the  melting  point 
by  increasing  pressure  has  been  accurately  investigated  by 
Tammann l  •  he  found  that  the  melting  point  of  monoclinic 
sulphur  and  the  transition  point  between  it  and  the  rhombic 
form  become  steadily  higher  with  increasing  pressure,  but  that 
the  second  rises  the  more  rapidly.  In  consequence  of  this,  the 
curves  representing  the  dependence  of  the  two  temperatures  on 
the  pressure  meet  at  a  pressure  of  1400  kg.  and  a  temperature 
of  152°.  At  this  junction  melting  point  and  transition  point  are 
identical,  and  beyond  it  the  transition  point  would  lie  above  the 
melting  point. 

Since  the  presence  of  a  foreign  admixture  lowers  the  melting 
point  of  a  substance,  if  the  former  is  soluble  in  the  fused  mass, 
it  follows  that  a  displacement  of  the  melting  point  below  the 
transition  point,  and  consequently  the  conversion  of  an  enantio- 
tropically  dimorphous  substance  into  a  monotropic  one,  can  also  be 
effected  by  means  of  such  an  addition.  A  conversion  of  this 
kind  was  first  obtained  by  Schenck  and  Schneider2  in  the  case  of 
p-azoxyanisole,  which  at  116-8°  undergoes  transformation  into  a 
second  and  "liquid  crystalline"  modification,  which  in  its  turn 
melts  at  134°,  i.e.,  it  forms  then  a  truly  isotropic  liquid.  By 
addition  of  benzophenone  this  melting  point  can  be  lowered  as  far 
as  108-4°,  that  is  to  say  8-4°  below  the  transition  temperature, 
so  that  the  substance  then  behaves  as  a  monotropically  dimorphous 
one.  Carbon  tetrabromide,  CBr4,  crystallises  after  fusion  (m.p. 
92-5°)  in  cubic  crystals,  which  at  46-9°  become  transformed  into 
the  monoclinic  modification  which  is  stable  at  ordinary  tem- 
peratures ;  according  to  the  investigations  of  Rothmund 3  this  transi  - 

1  Krystallisieren  und  Schmelzen,  269. 

-  Zeits.  f.  phys.  Chem.  1899,  29,  546  ;  Journ.  C.  S.  76,  ii.  637. 

;:  Zeits.  f.  phys.  Chem.  1897,  24,  712  ;  foum.   C.  S.  74,  ii.  158. 


CHEMICAL  CRYSTALLOGRAPHY 

tion  point  is  lowered  by  the  addition  of  carbon  tetrachloride, 
proportionally  to  the  quantity  of  the  latter,  to  the  extent  of  1-6 
for  2  mol.  per  cent.  Since  carbon  tetrachloride  is  liquid,  and 
solidifies,  even  below  o°,  only  under  high  pressure,  it  is 
probable  that  the  lowering  of  the  melting  point  of  carbon  tetra- 
bromide,  by  addition  of  the  chloride,  is  much  greater  than  that 
of  the  transition  point,  and  a  moderate  addition  of  tetrachloride 
might  suffice  to  convert  the  enantiotropically  dimorphous  tetra» 
bromide  into  a  monotropically  dimorphous  substance. 

Just  as,  in  a  greatly  overcooled  liquid,  the  internal 
friction*  in  many  cases  becomes  so  great  that  the  growth 
of  crystals  in  it  can  take  place  only  with  extreme  slowness, 
it  is  likewise  found,  in  the  transformation  of  polymorphous 
substances  from  one  modification  into  another,  that,  though 
the  rate  of  transformation  certainly  increases  when  over- 
cooling  below  the  normal  transition  point  has  taken  place, 
it  nevertheless  reaches  a  maximum  at  a  certain  degree  of 
supercooling  ;  beyond  this  point  the  rate  diminishes  again. 
Gernez  (see  page  19)  has  proved  this  behaviour  in  the  case 
of  enantiotropic  sulphur,  and  Schaum  [  found  that  the  two 
modifications  of  the  monotropically  dimorphous  hexachloro- 
keto-dihydrobenzene,  CGC16O,  when  their  formation  had 
been  brought  about  in  the  one  preparation  of  the  substance, 
could  at  ordinary  temperatures  exist  unchanged  for  years 
in  contact  with  one  another  ;  whilst,  on  gently  warming 
the  preparation,  the  transformation  immediately  proceeded. 
In  this  respect  also,  therefore,  these  two  kinds  of  poly- 
morphous substances  appear  not  to  be  different. 

The  simultaneous  formation  of  different  polymorphous 
modifications  in  a  solution  is  a  phenomenon  which  is  at  least 
analogous  to  the  above-mentioned  indifference  towards 
direct  transformation  ;  the  following  substances  exhibit 
this  peculiarity  : — 

Telluric  acid,  H(JTeOc,  crystallises  both    cubic  (in   octahedra) 

and  monoclinic  (in  pseudo-trigonal  doublets  and  triplets).     From 

hot  nitrir  arid  of  a  certain  concentration  both  modifications  are 

formed  side  by  side;  a  gradual  transformation  of  the  mbir  form 

:  >  t'-ti  ,/••>   I \rnnrr if i  47, 


POLYMORPHISM  29 

into  the  monoclinic  takes  place  only  with  dilution  of  the  nitric  acid. 
In  the  dry  state  both  forms  are  very  stable,  and  no  transforma- 
tion of  the  one  into  the  other  takes  place.1 

Ammonium  fluosilicate,  (XH4)._,SiF6,  crystallises  from  aqueous 
solution  at  temperatures  above  13',  cubic,  and  below  6",  hexagonal  ; 
between  these  two  temperatures  both  modifications  are  formed 
side  by  side,  and  undergo  no  alteration  at  ordinary  temperature  ; 
the  hexagonal  form  becomes  transformed  into  the  cubic  only  when 
it  is  heated  along  with  some  of  the  solution  on  the  water  bath. 
In  the  dry  state  both  modifications  can  exist  side  by  side  for  an 
indefinite  period,  provided  the  temperature  is  not  high ;  only 
towards  locf  do  the  hexagonal  crystals  fall  to  a  powder,  which 
probably  consists  of  the  cubic  form.2 

Di-m-nitro-s-diphenylcarbamide,  CO(NH.CKH4NOo).,,  exists  in 
three  modifications  :  a,  yellow  prismatic  crystals  ;  /3,  white  needles  ; 
7,  yellow  tablets.  When  a  solution  of  one  of  these  forms,  or  of  a 
mixture  of  them,  is  prepared  in  boiling  alcohol  of  95  per  cent., 
and,  after  having  been  filtered  while  warm  into  a  flask  kept  at 
constant  temperature  by  immersion  in  an  oil  bath,  is  caused 
slowly  to  evaporate  by  leading  through  it  a  current  of  dry  air, 
then,  between  75°  and  30°,  crystals  of  the  a  and  £  modifications  are 
always  obtained  side  by  side,  even  when  the  solution,  saturated 
at  the  given  temperature,  has  been  inoculated  with  crystals  of  one 
kind.  At  the  higher  temperatures  more  crystals  of  the  a  modifica- 
tion are  obtained;  at  the  lower  ones,  more  of  /8.  Specially  good 
crystals  are  obtained  at  6cr.  The  inoculation  with  crystals  of 
one  kind  merely  results  in  increasing  and  accelerating  the 
separation  of  that  particular  form,  with  retardation  of  the  forma- 
tion of  the  other  one  ;  in  this  way,  however,  the  development 
of  specially  good  crystals  of  the  second  form  is  favoured.  If  the 
filtered  mother-liquor  is  allowed  to  evaporate  by  exposure  to  air  at 
the  ordinary  temperature  (13°),  then  the  third  modification,  7,  alone 
crystallises  out.  If  the  solution  is  warmed  a  few  degrees,  however, 
then  a  few  crystals  of  /3  also  appear  ;  at  40  ,  7  entirely  disappears, 
and  a  appears  in  small  quantities,  increasing  with  rising  tempera- 
ture. Accordingly,  so  far  as  separation  from  alcoholic  solution 
is  concerned,  the  y  modification  is  the  most  stable  at  ordinary 
temperatures,  the  form  3  at  50-60°,  and  «  at  higher  temperatures. 
This  behaviour  may  be  modified  by  the  solvent,  however  ;  for,  from 

1  Gossner,  Zfits.f.  Kryst.  1903,  38,  501. 
'-'  Goisner,  loc.  at.  147. 


30  CHEMICAL  CRYSTALLOGfcAPHY 

glacial  acetic  acid,  or  from  a  mixture  of  it  with  alcohol,  only  the 
white  needles  of  p  are  obtained  on  cooling,  and  such  is  also  the 
case  on  preparation  in  presence  of  hydrochloric  acid.  If  the 
7  crystals  are  heated  to  60°,  they  become  opaque  and  then  white  ; 
towards  180°,  the  /3  crystals  become  opaque  and  then  yellow  ;  the 
o  crystals  melt  at  242°  without  previous  change,  and  this  tem- 
perature is  also  the  melting  point  of  the  transformation  products 
of  the  ft  and  y  modifications.1 

The  following  can  also  be  obtained  side  by  side  from  solu- 
tions:—The  rhombic  and  the  monoclinic  modification  of  sodium 
beryllium  fluoride  (Xa.jBeF4)2  ;  the  two  forms,  entirely  different  in 
structure,  of  dimethylammonium  chloroplatinate  (NHo(CH3)2)oPtCl6, 
according  to  le  Bel3;  the  monoclinic  and  the  triclinic  modi- 
fication of  rubidium  bichromate,  RboCr.jO7, 4  ;  the  two  forms 
of  ammonium  paratungstate,  (NH4)10\V12O4i,HoO 5  ;  of  mannitol, 
C6H14O6°;  of  /H-diamidobenzenesulphonic  acid,  C6H3(NH3>.jSOaH,7 
etc. 

In  these  and  many  other  cases,  the  direct  transformation  of  the 
one  crystallised  modification  into  the  other  has  not  been  proved — 
as  a  rule,  no  attempt  has  been  made  to  do  so.  Since,  further,  for 
most  of  the  substances  (especially  the  organic  ones)  which  are 
known  in  different  crystalline  forms,  the  densities  of  the  two  modi- 
fications are  unknown,  it  is  possible  that  in  some  of  the  cases  we 
have  to  deal  with  polysymmetric  substances,  especially  when  the 
two  forms  correspond  to  very  similar  crystal  structures.  This  is 
the  case,  for  example,  with  the  two  modifications  of  the  above- 
noted  examples  of  ammonium  paratungstate  and  of  mannitol  ; 
also  with  the  monoclinic  compound  CuNO;5OH,Cu(OH)o  (prepared 
by  Wells  and  Penfield),  whose  density  differs  but  slightly  from 
that  (which  probably  could  be  only  approximately  determined) 
of  the  rhombic  mineral,  gerhardtite,  which  crystallises  quite 

1  Offret  and  Vittenet,  Bull,  soc.fr.  tnin.  1899,  22,  69;  Ails.  f.  Kryst. 
'901,  34,  627  ;  Journ.  C.  S.  76,  I,  886. 

a  Marignac,  Arch,  sc.phys.  nat.  1873,  46,  196  ;  Journ.  C.  S.  27,  24. 
3  See  Ries,  Zeils.f.  A'ryst.  1902,  36,  330. 

4Wyrouboff,  Butt,  soc.fr.  min.  1881,  4,  120;  Zeits.  f.  Kryst.  8, 
639. 

*  Marignac,  Ann.  Chim.fhys.  1863  [3],  69,  24. 

*  Zeph  ••••'>•/  AVys/.  i8S8,  13,  145. 


POLYMORPHISM  31 

similarly l ;    undoubtedly    polysymmetric    (trigonal    and    pseudo- 
trigonal)  is  cerium  silicotungstate,  Ce^WjoSiO^SiHoO.3 

It  has  already  been  stated  on  page  16  that,  as  a  rule, 
that  modification  of  a  polymorphous  substance  which  is 
stable  at  higher  temperatures  possesses  the  lower  density,  and 
such,  as  a  matter  of  fact,  is  the  case  for  the  following 
among  the  examples  already  fully  treated,  namely — Sulphur 
(page  17),  mercuric  iodide  (page  19),  and  hexachlorethane 
(page  20)  ;  and,  in  addition,  for  quarz  and  tridymite,  as 
also  for  a  series  of  other  substances  for  which  the  densities 
of  the  different  modifications  are  known.  On  the  other 
hand,  there  has  been  already  mentioned  (page  21)  a  sub- 
stance, ammonium  nitrate,  which  shows  the  opposite 
character.  It  is  true  that  the  transformation  of  the  first 
rhombic  modification  into  the  second  rhombic  one  follows 
the  above  rule,  but  the  transformation  of  the  second 
rhombic  modification  into  the  trigonal  one  is  accompanied 
by  an  increase  of  density.  The  same  is  the  case  with 
the  transformation  of  trigonal  silver  iodide,  Agl,  into 
the  cubic  form,  which  is  stable  at  higher  tempera- 
tures ;  also  with  dipropylammonium  chloroplatinate, 
(XH2(C3H7)2)2PtCIG,  which,  according  to  Ries,  forms 
two  monoclinic  modifications  of  totally  different  crystal 
structure  ;  further,  also,  with  the  transformation  of 
boracite  into  the  cubic  form  (page  9),  and  of  the  mono- 
clinic  calcium  chloraluminate  into  the  trigonal  modification 
(page  9).  Analogous  cases,  in  which  the  modification 
corresponding  to  the  higher  temperature  is  likewise  the 
denser,  are  those  of  arsenious  oxide,  As^  ;  antimonious 
oxide,  Sb4O6  ;  also  calcite  and  aragonite,  CaCO3  ;  potassium 
calcium  chromate,  K2Ca(CrO4)2,2H2O  ;  and,  among  the 
elements,  phosphorus  and  arsenic  (whilst  carbon  is  normal). 
Since,  amongst  the  above-mentioned  polymorphous  sub- 
stances of  the  second  kind,  there  are  cases,  such  as  those  of 

1  Zeits.f.  Kryst.  1887,  II,  303. 

~  Wyrouboff,  Bull.  soc.  //-.  min.   1896,  19,  219  et  sey.  ;    Zeits.  f.  A'rvst. 
29,  667. 


CHEMICAL  CRYSTALLOGRAPHY 

silver  iodide  and  boracite,  in  which  the  modification  which  is 
stable  at  higher  temperatures  belongs  to  the  cubic  system, 
or,  at  least,  possesses  higher  symmetry  than  the  other 
modification,  as  in  the  case  of  ammonium  nitrate  and 
calcium  chloraluminate,  it  might  be  supposed  that  the 
contraction  on  transformation  was  caused  by  the  assump- 
tion of  higher  symmetry  of  crystal  structure,  with  a  resultant 
denser  arrangement.  This,  however,  is  contradicted  by 
the  knowledge  that,  with  phosphorus,  arsenic,  arsenious 
oxide,  and  antimonious  oxide,  as  well  as  with  calcium  car- 
bonate, precisely  the  reverse  is  the  case,  since  with  them 
the  modifications  which  are  stable  at  lower  temperature 
possess  the  higher  symmetry  and  the  lower  density. 

Quite  similar  relations  are  found  with  those  substances 
which  follow  the  first-mentioned  rule  :  the  form  with  higher 
symmetry  may  possess  the  higher  density,  and  consequently 
correspond  to  the  lower  temperature,  as  in  the  cases  of 
carbon,  sulphur,  tin  (tetragonal  and  rhombic),  and  mercuric 
iodide  ;  or  the  form  stable  at  higher  temperatures,  and  pos- 
sessing the  lower  density,  may  exhibit  a  higher  symmetry, 
as,  for  example,  the  cubic  modification  of  telluric  acid,  of 
ammonium  and  potassium  fluosilicates,  of  hexachlorethane, 
of  ammonium  nitrate  (as  compared  with  the  trigonal  or 
hexagonal  modification).  Similarly,  the  monoclinic  form 
of  carbon  tetrabromide  becomes  transformed  at  46-9°  into  a 
cubic  modification,  with  considerable  increase  of  volume 
(Steinmetz) ;  and  various  polymorphous  chloroplatinates 
behave  similarly,  according  to  the  investigations  of  Ries. 

The  number  of  polymorphous  substances  which  become 
transformed  at  higher  temperatures  into  a  cubic  (singly 
refracting)  modification  is  strikingly  large ;  but,  as  the  above 
examples  show,  this  may  be  accompanied  by  either  an  in- 
crease or  a  decrease  of  volume.  The  former  case  is  the  com- 
moner, evidently  because  the  majority  of  substances  follow 
the  rule  that  the  form  corresponding  to  the  higher  tempera- 
ture possesses  the  lower  density.  On  the  other  hand  there 
also  L\M.  in  both  ila^o  <»f  "iib-tamc-,  cases  where  the 


POLYMORPHISM  33 

modification  corresponding  to  the  lower  temperature  crystal- 
lises in  the  cubic  system. 

As  in  the  matter  of  symmetry,  so  also  in  the  matter  of 
the  crystallographic  dimensions,  is  it  found  that  the  relations 
between  the  different  modifications  of  polymorphous  sub- 
stances are  very  various.  In  many  there  is  an  evident 
similarity  in  the  crystal  structures  of  the  two  modifications.1 

Carbon  tetrabroraide,  CBr4  (page  32),  crystallises  at  ordinary 
temperatures  in  monoclinic  crystals,  whose  shape  differs  from  that 
of  a  regular  octahedron  (tabular  on  one  pair  of  faces)  only  by  very 
small  variations  in  the  angles,  and  which  cleave  parallel  to  the  pre- 
dominating pseudo-octahedral  face.  At  46-9°  the  crystals  become 
singly  refracting,  without  losing  their  transparency,  and  conse- 
quently have  undergone  transformation  into  truly  regular  octa- 
hedra. 

p-Nitrophenol,  CcH4OHNOo,  crystallises  at  ordinary  tempera- 
tures in  monoclinic  prisms  ;  from  warm  solutions  and  from  the 
fused  substance  a  modification  which  is  metastable  at  ordinary 
temperatures  is  obtained,  consisting  of  prisms  whose  angles  are 
almost  identical  with  the  prism  angles  of  the  stable  modification  ; 
the  axial  inclinations  of  the  two  forms  likewise  differ  but  little  from 
one  another,  and  the  c  parameters  stand  almost  exactly  in  the  ratio 
2  :  I,  so  that  the  two  substances  were  assumed  by  earlier  investi- 
gators to  be  identical.  Naturally,  they  differ  as  regards  their 
physical  properties,  cleavage,  optical  behaviour,  etc.2 

Mannitol  (page  30)  exists  in  two  rhombic  modifications  of  very 
similar  form,  possessing  the  same  cleavage  ;  their  mutual  relations 
require  further  investigation,  however. 

Finally,  attention  may  be  called  to  Beckenkamp's  views  regard- 
ing the  relationships  between  the  crystal  structures  of  quarz  and 
tridymite.3 

The  number  of  such  examples  might  be  further  increased  by 
numerous  cases  in  which  conclusions  regarding  the  form  of  the 
one  modification  can  be  drawn  only  indirectly  from  that  of  some 
chemically  analogous  substance  ;  in  any  case  the  relations  between 

1  The  inevitable  similarity  between  those  forms  which  stand  to  one 
another  in  the  relation  of  polysymmetry  naturally  does  not  come  into  con- 
sideration here  ;  only  that  between  truly  polymorphous  modifications. 

2  O.  Lehman n.  ZeUs.  /.  Kryst.  1877,  I,  45. 
*  Zeits.  /.  Kryst.  1901.  34,  579  tt  seq. 

C 


CHF.MICAI.  CRYSTALLOGRAPHY 

the  cubic  and  the    pseudo-cubic    modifications    of   phosphorus, 
arsenic,  boracite,  leucite,  etc.,  fall  also  to  be  included  here. 

On  the  other  hand,  the  closer  investigation  of  the 
various  modifications  of  a  substance  generally  shows  that, 
even  where  certain  similarities  between  the  angles  occur, 
there  are  always  profound  differences  observable — in  the 
cohesion,  with  respect  to  the  crystal  forms  specially  favoured 
during  the  growth  of  the  crystal,  and  in  other  properties  — 
which  point  to  an  essential  difference  of  crystal  structure  in 
the  various  modifications. 

The  reason  why,  as  yet,  no  general  rules  governing  the 
relations  between  the  crystal  structures  of  the  different 
modifications  of  a  polymorphous  substance  have  been  recog- 
nised, is  to  be  sought  in  the  fact  that,  so  far,  there  are  only 
a  very  small  number  of  substances  whose  different  modifica- 
tions have  been  studied  so  fully,  from  the  crystallographical 
point  of  view,  that  a  decision  regarding  their  crystal  struc- 
ture can  be  arrived  at  with  some  degree  of  probability  ;  the 
list  at  present  consists  almost  entirely  of  isolated  examples. 
An  insight  into  the  regularities  which  doubtless  exist  would 
be  possible  only  if  there  were  accurate  physico-crystallo- 
graphical  investigations  of  the  various  crystalline  modifica- 
tions of  different  series  of  substances  which  exhibit,  as 
regards  their  chemical  constitution,  close  relations  of  a 
well  recognised  nature.  In  any  such  systematic  investiga- 
tion of  these  questions  difficulties  would  certainly  arise  in 
many  cases,  owing  to  the  circumstance  that  for  two  chemi- 
cally related  substances,  even  when  they  possess  a  quite 
analogous  constitution,  the  limits  of  temperature  and  pres- 
sure within  which  their  different  modifications  are  stable 
may  differ  very  greatly  from  one  another.  This  is  generally 
the  case,  for  example,  with  the  analogous  compounds  of 
chlorine,  bromine,  and  iodine.  Among  these,  the  com- 
pounds of  iodine  generally  possess  the  highest  melting  point, 
other  conditions  being  the  same  ;  consequently,  for  many 
iodine  compounds  the  transition  temperature  between  two 
modifications  lies  above  the  ordinary  temperature,  whilst 


POLYMORPHISM  35 

for  the  corresponding  chlorine  and  bromine  compounds 
it  lies  much  below  the  ordinary  temperature.  As  a  result, 
the  iodine  compound  is  obtained  under  ordinary  conditions 
in  a  form  which,  when  heated,  undergoes  transformation 
into  a  new  modification  before  melting.  Those  forms  of  the 
chlorine  and  bromine  compounds  which  correspond  to  the 
first  modification  of  the  iodine  compound,  would  be  formed 
only  at  a  temperature  so  low  that  proof  of  the  transformation, 
and  crystallographic  examination  of  the  new  form,  would  no 
longer  be  possible.  Since  monotropic  modifications  melt  at 
different  temperatures,  it  may  well  be  that  the  anomalies 
as  regards  melting  point,  observable  with  many  organic  com- 
pounds, are  in  most  cases  due  to  the  fact  that  the  anomalous 
melting  point  is  that  of  a  different  modification. 


THE  COMPARISON  OF  THE  CRYSTAL 
STRUCTURES  OF  CHEMICALLY 
ALLIED  SUBSTANCES  (MORPHO- 
TROPY) 

THE  recognition  of  the  laws  governing  the  dependence  of 
the  crystal  structure  of  a  substance  on  its  chemical  constitu- 
tion, forms  the  ultimate  goal  of  chemical  crystallographical 
research.  The  road  thereto  can  be  found  only  by  com- 
parison of  the  crystal  structures  of  numerous  series  of 
chemically  allied  substances.  Since,  however,  substances  in 
general  are  capable  of  assuming  different  crystal  structures 
under  different  conditions,  the  relationships  between  the 
structures  of  two  substances  can,  naturally,  be  recognised 
only  when  the  corresponding  states  of  the  two  are 
compared.  For  the  reasons  given  at  the  end  of  the  pre- 
ceding section,  however,  these  are  in  many  cases  unob- 
tainable ;  or,  at  least,  the  properties  of  the  one  substance  in 
that  state  cannot  be  determined  so  completely  as  to  allow 
of  its  crystal  structure  being  deduced  therefrom  with  any- 
thing like  probability.  In  spite  of  these  difficulties,  and  the 
consequent  incomplete  character  of  the  material  available 
for  comparison,  it  has  nevertheless  been  possible  to  recognise 
certain  relationships  between  the  crystal  forms  of  substances 
whose  chemical  constitution  exhibits  a  definite  relationship  ; 
and,  as  might  be  expected,  the  connection  is  the  more 
intimate,  and  therefore  the  more  striking,  the  closer  the 
substances  concerned  stand  to  one  another  as  regards 
chemical  character.  Hence  it  arose  that  the  cases  in 


MORPHOTROPY  37 

which  the  close  agreement  in  crystal  structure  was  first 
recognised  were  those  of  substances  whose  chemical 
constitution  exhibits  complete  analogy,  e.g.,  that  of  two 
salts  formed  by  the  same  acid  with  two  closely  related 
metals  of  like  valency,  or  that  of  two  salts  of  the  same 
metal  with  two  completely  analogous  acids,  such  as  ortho- 
phosphoric  and  ortho-arsenic  acids.  This  agreement  was 
called  isomorphism  by  its  discoverer,  Mitscherlich  ;  it 
will  receive  detailed  treatment  further  on. 

In  general,  the  question  as  to  the  relation  between  the 
crystal  structures  of  two  substances,  which  stand  in  definite 
chemical  relationship  to  one  another  and  which  are  known 
in  corresponding  states,  will  be  answered  when  it  can  be 
stated  what  change  the  crystal  structure  of  the  one  sub- 
stance undergoes  when  those  changes  in  the  chemical 
molecule,  by  which  it  is  transformed  into  the  second  sub- 
stance, are  imagined  to  be  carried  out.  This  change  in 
the  crystal  structure  can  be  looked  upon  as  the  analogue 
of  a  homogeneous  deformation,  since  by  it  a  homogeneous 
system  —  the  crystal  structure  of  the  first  substance — is 
converted  into  a  second,  likewise  homogeneous,  system — 
the  crystal  structure  of  the  second  substance. 

According  to  the  theoretical  views  to  which  the  study 
of  the  physical  properties  of  crystals  has  led,  the  essence  of 
the  crystal  structure  of  a  substance  is  the  fundamental  space 
lattice,  i.e.,  the  arrangement  of  homologous  points,  such  as 
all  similar  and  similarly  orientated  atoms.  But  from  a 
knowledge,  as  complete  as  may  be,  of  the  assemblage  of 
crystal  faces  of  a  substance,  from  its  cohesion,  twinning,  etc., 
we  are  enabled  to  decide  as  to  the  most  probable  form  of 
the  space  lattice.  If,  now,  we  refer  the  faces  of  the  crystal 
to  the  planes  of  the  appropriate  primitive  parallelepiped, 
then  the  so-called  crystal  elements  (i.e.,  the  parametral 
ratios  a  :  b  :  c,  and  the  axial  angles  a,  /3,  y)  simultaneously 
give  us  the  relative  lengths  of  the  sides  of  the  parallelepiped, 
and  its  angles.  If  now  we  imagine  the  space  occupied  by 
the  structure  of  the  crystal  to  be  divided  into  space  units 


38  CHEMICAL  CRYSTALLOGRAPHY 

such  that  in  each  there  are  contained  the  atoms  correspond- 
ing to  a  chemical  molecule,  then,  naturally,  the  centres  of 
gravity  of  these  space  units  form  the  same  space  lattice,  and, 
with  the  proviso  made  above,  the  parameters  of  the  crystal 
determine  the  relative  distances  of  these  centres  from  one 
another. 

The  usual  crystallographic  axial  ratios,  however,  state 
these  relative  dimensions  for  each  substance  in  such  a  way 
that  one  of  them  serves  as  unit,  whilst  the  relation  in  which 
this  unit  stands  to  that  for  any  other  substance  remains 
unknown.  From  considerations  which  were  advanced 
simultaneously  by  Becke  and  by  Muthmann l  (in  the  first 
instance,  however,  only  with  a  limitation  to  isomorphous 
substances,  ?>.,  such  as  stand  to  one  another  in  the 
relation  of  isomorphism,  as  mentioned  on  the  previous 
page),  there  appears  to  exist  a  possibility  of  determining 
the  ratio  of  these  units  for  different  substances  which  it  is 
desired  to  compare  with  one  another,  or,  in  other  words, 
of  referring  to  the  same  unit  the  relative  distances  between 
homologous  points  in  the  structures  of  such  substances. 

The  space  units  (as  defined  above)  of  the  crystal  structures 
of  two  different  substances  contain  each  a  chemical  molecule 
of  the  respective  substances  ;  their  masses  must  therefore 
stand-in  the  same  ratio  to  one  another  as  the  molecular 
weights  of  the  two  substances.  If,  now,  we  assume  two 
crystallised  substances  to  have  the  same  density  d,  but 
different  molecular  weights,  M  and  M'  respectively,  it  is 
evident  that  the  volumes  of  the  space  units  of  their  crystal 
structures  must  be  in  the  proportion  of  the  molecular 
weights ;  for  a  given  volume  of  the  one  substance,  which, 
let  us  say,  possesses  a  molecular  weight  twice  that  of  the 
other,  would  then  consist  of  only  half  as  many  space  units 

1  F.   Uecke,   "  Ueber   Molekularc  Axenverhaltnisse,"  Anzeiger  d.  A'. 

Akad.   d.    Wiss.    Wien.    1893,   30,    204.     VV.    Muthmann,    "  Beitrage   zur 

Volumtheorie  der  krystallisierten  Kflrper,"  Zctts.  f.   A'ryst.  1894,22,  497. 

!    Kr.ius   and   G.    Mez,  "  Tber  topisrhe  Axcnverhiiltnis^e,"  Xeits.  /. 

A'ryi/.  1901,34,  389- 


MORPHOTROPY  39 

as  the  same  volume  of  the  other  substance,  so  that  the 
space  units  of  the  latter  must  be  twice  as  large.  If,  on  the 
other  hand,  the  molecular  weights  of  two  crystallised  sub- 
stances were  the  same,  but  their  densities,  d  and  d ',  different 
— say,  the  one  double  the  other — then  a  given  volume  of 
the  substance  with  the  higher  density  would  contain  twice 
as  many  space  units  as  the  same  volume  of  the  other  ;  the 
space  units  of  the  latter  would  therefore  be  only  half  the 
size  of  the  former,  or,  stated  generally  :  the  volume  of  the 
space  unit  is  inversely  proportional  to  the  density,  d.  If 
the  volumes  of  the  space  units  of  the  crystal  structures  of 
two  substances  are  designated  by  V  and  V,  then  the 
relationship  between  them  is  expressed  by  the  equation 

V  :  V  =  M  Id  :  M' /  d' 

i.e.,  The  volumes  of  the  space  units  in  the  crystal  structures 
of  different  substances  are  proportional  to  the  quotients 
obtained  by  dividing  the  molecular  weights  of  the  substances 
by  the  densities.  These  quotients  are  called  the  equivalent 
volumes  (or  molecular  volumes)  of  the  substances. 

If  the  volume,  V,  of  the  space  unit  of  the  crystal  structure 
of  each  crystallised  substance  is  taken  as  equal  to  its  equivalent 
volume,  the  volumes  of  these  space  units  are  thereby  referred 
to  the  same  unit,  namely  to  the  space  unit  of  a  crystallised 
substance  with  molecular  weight  equal  to  its  density,  for  in 
this  case  V=  i.  If  this  space  unit  had  the  shape  of  a  cube, 
the  length  of  an  edge  would  be  the  appropriate  unit  of  length, 
and  to  this  unit  of  length  would  be  referred  the  parameters 
of  the  primitive  parallelepipeds  of  every  crystallised  sub- 
stance when  these  were  calculated  by  the  help  of  the  volume 
V,  as  determined  from  the  molecular  weight  and  the  density. 
These  values  are  called  the  topic  parameters  of  the  sub- 
stance, since  they  follow  from  the  manner  in  which  the  sub- 
stance fills  space  ;  they  are  indicated  by  the  symbols  x>  \^>  <"• 

The  shape  of  the  units,  into  which  the  whole  space 
occupied  by  the  crystal  is  to  be  imagined  as  divided, 
depends  on  the  nature  of  the  space  lattice  which  forms 


40 


CHEMICAL  CRYSTALLOGRAPHY 


the  foundation  of  the  structure,  and  the  calculation  of  the 
topic  parameters  varies  according  to  this  shape. 

i.  In  the  most  general  case,  that  of  a  triclinic  space  lattice,  it  is 
evident  that  the  shape  of  the  space  unit  is  identical  with  that  of 
the  elementary  parallelepiped  of  the  lattice.  For,  if  we  imagine 
the  space  occupied  to  be  divided  up  parallel  to  the  sides  of  this 
parallelepiped  into  equal  units  of  the  same  shape  and  size,  the 
centres  of  gravity  of  these  units  reproduce  an  exactly  similar 

space  lattice.  In  any  such 
parallelepiped  (Fig.  3)  let  the 
sides  EH  =  *,  EF  =  ^  and 
EJ  =  w,  and  further,  JS  be 
the  normal  to  the  basal 
plane  EFGH,  and  SN  per- 
pendicular to  EH  (so  that 
A  is  the  angle  between  the 

planes  EFGH  and  EHMJ),  then1  the  volume  of  the  parallelepiped 
is  given  by  the  equation 

V  =  x\j/u  sin/3  sin  7  sin  A. 

If  the  ratios  EH  :  EF  :  EJ  are  given  as  usual  by  the  crystallo- 
graphic  axial  ratios  a  :  i  :  c,  so  that  x  '  $  =  «,  and  w  :  ^  =  ^  then 
the  following  values  are  obtained  for  the  topic  parameters  :— 
*~  ^{V/ac  sin/3  sin7  sinA} 

X   =  a\f/  =     J{a2V  /  c  sin /3  sin 7  sin  A} 
w  =  c\f/   =    £/{c*V  I  a  sin/3  sin  7  sin  A}. 

2.^If  the  space  lattice  is  monoclinic,  with  the  angles  A,  u,  and 
7  =  90°  (Fig.  4),  then  the  above  equations  reduce  to  the  following  : — 
X   =   at  =      */fa*V  /  c  sin  J3} 

sin/3} 
r  sin/3}. 

3.  If  the  elementary  parallelepiped  has  the 
form  of  a  rhombic  prism  with  oblique  base, 
the  same  formula  ^ive  x  and  ^  as  the  diagonals 
of  the  base,  and  from  these  the  sides  follow 
directly,  whilst  w  is  the  height.  As  is  evident 
from  Fig.  4,  the  volume  of  this  prism  is 
exactly  half  of  that  of  the  parallelepiped  KFC.HJKLM. 
1  Krau:  and  Mez.  /,  . 


FIG.  4. 


MORPHOTROPY  41 

4.  If  the  elementary  parallelepiped  is  rectangular  (corre- 
sponding to  the  rhombic  system),  then  the  lengths  of  its  three 
sides  are  :  — 

X  =  a* 


<»  =  <:*  =     J{'*V/a}. 

5.  In  the  case  of  a  rhombic  prism  with  right  base,  there  is  the 
same  relation  between  this  parallelepiped  and  the  preceding  one, 
as  was  shown  between  cases  3  and  2  ;    it  is  only  necessary  to 
suppose,   in    Fig.   4,   the    sides  JM,    KL,   etc.,  perpendicular  to 
EJ,  etc. 

6.  From  the  rectangular  parallelepiped  space  lattice  another 
can    be    derived,    in    which    the    centres   of  the    parallelepipeds 
also  are   points  of   the    lattice.1      If  we   imagine  all  the  points 
of   such    a    lattice    as    middle    points   of  the    space    units,   then 
these    no    longer    have    the   form    of   a    triparallelohedron,    con- 
sisting of  three  pairs  of  parallel  planes,  which  so  far  has  been  the 
only  case  considered,  but  of  a  heptaparallelohedron  corresponding 
to  a  combination  of  a  rhombic  bi-pyramid  with  the  three  pinacoids 
(see  under  12).     The  volume  of  this  unit  is  just  half  of  that  of  the 
rectangular  parallelepiped,  for  the  number  of  lattice  points  in  a 
given  space  is  twice  as  great  as  in  the  rectangular  parallelepiped 
lattice. 

7.  From   the   space   lattice    5    still   another   can   be    similarly 
derived,  in  which  the  lattice  points  form  the  corners  of  rhombic 
bi-pyramids.2     If  these  are  imagined  as  centres   of  space  units, 
the   latter    will   then    have    the   form   of   a   hexaparallelohedron, 
corresponding  to  a   combination   of   the    three    rhombic    prisms 
{no},  {  ioi  },   {011}  (see  under  13).      The  volume  of  this   unit 
is  half  of  that  of  the  corresponding  rhombic  prism,  since  twice 
as  many  of  them  are  contained  in  the  same  space. 

8.  In  the   tetragonal   prismatic   space   lattice   the   elementary 
parallelepiped  is  again  rectangular,  and  a  -  b  ;  consequently 


1  Physikalische  Krystallographie,  third  edition,  fig.  140  </;  fourth  edition, 
fig.  156  d. 

-  Phys.  Am/.,  third  edition,  fig.  140  A  ;  fourth  edition,  fig.  156  b. 


42  CHEMICAL  CRYSTALLOGRAPHY 

9.  If  the  centres  also  of  the  prisms  are   lattice  points,  then 
twice    as   many   of  these   are   present ;    the   space   units  (which, 
consequently,  are  only  half  the  size)  are  hexaparallelohedra,  cor- 
responding to  a  combination  of  the  tetragonal  prism  {no}  and 
the  bi-pyramid  of  the  second  kind  { 101 }. 

10.  In   the   rhombohedral   space   lattice,   and   the   triparallelo- 
hedral  space  unit  identified  with  it,  we  have,  for  the  sides,  a  =  b  =  c 
and,  for  the  angles,  a=p  =  y  ;  consequently 

X   =    \f/   =   u   =  N3/[V/ sin-a  sin  A|, 

where  A  is  the  supplement  of  the  measured  angle  between  the  faces 

of  a  polar  edge  of  the  rhombohedron,  and  is  given  by  the  equation, 

sin  (A/2)   =   sin  (a/2)  j  sin  a. 

11.  In    the    cubic    space    lattice,   a  =  b=c  and   a  =  /3  =  7  =  9oc  ; 
consequently 

x  =  ^  =  „  =   y  v. 

As  mentioned  on  page  39,  the  three  topic  parameters  of  such 
a  space  unit  would  assume  the  value  i  if  V=  i,  i.e.,  if  the  molecular 
weight  were  equal  to  the  density. 

12.  If  two  cubic  space  lattices  are  placed  the  one  within  the 
other,  so  that  the  points  of  the  one  form  the  centres  of  the  cubes  of 
the  other,  that  lattice  is  obtained  which  possesses  the   densest 
arrangement  in  the  planes  of  the  rhombic  dodecahedron.1     The 
points  of  this  space  lattice  form  the  centres  of  heptaparallelohedra 
having  the  shape  of  a  cubo-octahedron- ;  its  volume  is,  naturally, 
the  half  of  the  corresponding  hexahedron. 

By  a  homogeneous  deformation,  resulting  in  the  lengths  of  the 
three  sides  of  the  cube  becoming  unequally  lengthened,  this  hepta- 
parallelohedron  passes  into  that  mentioned  under  6. 

13.  The  space  lattice  which  possesses  closest  packing  in  the 
octahedral  planes,  and  which  is  formed  from  four  simple  cubic 
space   lattices,3  gives   a   space  unit  whose  volume  is   only   one- 
fourth  of  that  of  the  simple  cubic  space  unit,  and  whose  shape 
is  that  of  a  rhombic   dodecahedron   having  its  three  tetragonal 
axes  equal  in  length  to  the  edges  of  the  circumscribed  cube. 

A  homogeneous  deformation  by  which  only  the  length  of  one 

1  /'A\-t.  A'r\  v/.,  third- edition,  fig.  144  b  •  fourth  edition,  fig.  160  t>. 
'-'  /V/vr.  A;;v5/.,  third  edition,  fig.  152  ;  fourth  edition,  fig.  148. 

•    •/..  third  edition,  fi^.  144  ,- ;  fourth  edition,  fiir.  160  r. 


MORPHOTUOPY  43 

of  these  axes  is  affected  gives  rise  to  the  hexaparallelohedron 
mentioned  under  9  ;  whilst  a  deformation  resulting  in  all  three 
axes  becoming  unequal  gives  rise  to  that  mentioned  under  7. 

14.  A  peculiar  position  is  occupied  by  the  hexagonal  space 
lattice,  in  which  the  points  lie  at  the  corners  of  a  trigonal 
prism.  The  lattice  points  form  the  centres  of  space  units  whose 
shape  is  that  of  a  hexagonal  prism.  If  the  ratio  of  w,  the  height 
of  this  prism  (the  principal  axis),  to  x,  the  distance  between 
opposite  corners  of  the  base  (a  lateral  axis),  is  expressed  by  c, 
it  follows  that 

sin  60* 


w   =  cx  =    Z/{V<?}  /  sin  60°. 

By  a  homogeneous  deformation  resulting  in  a  slight  lengthening 
or  shortening  in  the  direction  of  the  normal  to  the  front  prism  face, 
the  hexagonal  prism  changes  into  the  pseudo-hexagonal  combina- 
tion of  a  pinacoid  and  a  prism  with  a  basal  plane,  whose  three 
diagonals  are  now  no  longer  exactly  equal  ;  two  of  these  have 
the  same  length,  which  may  be  designated  by  x>  and  make  equal 
angles,  of  about  30°,  with  the  axis  of  deformation  ;  the  third, 
whose  length  may  be  taken  as  \f/,  is  normal  to  the  bisector  of 
the  angle  between  the  other  two.  Such  a  space  unit  corresponds 
to  the  rhombic  prismatic  space  lattice,  and  its  dimensions  can 
be  easily  calculated  from  the  rectangular  parallelepiped  whose  sides 
are  in  the  same  proportion  as  the  crystallographic  axes,  a,  <£,  <;, 
and  whose  volume  is  double  that  of  the  former. 

If  the  deformation  axis  is  inclined  to  the  normal  of  the  front 
prism  face  of  the  hexagonal  prism,  but  lies  in  the  vertical  plane, 
there  results  the  pseudo-hexagonal  monoclinic  combination, 
analogous  to  the  preceding  one,  and  the  calculation  follows 
from  the  corresponding  parallelepiped,  as  before,  except  that  now 
the  sides  proportional  to  a  and  c  form  the  oblique  angle  p.  The 
ratio  of  the  volume  of  this  parallelepiped  to  the  pseudo-hexagonal 
prism  is  unaffected  by  the  homogeneous  deformation. 

If,  lastly,  the  deformation  of  the  hexagonal  prism  leads  to  the 
triclinic  combination  of  three  pairs  of  parallel  planes  intersecting 
at  nearly  equal  angles,  then  the  base  has  three  unequal  and 
unequally  inclined  diagonals  x>  ^  and  ^'.  The  calculation  of 
these  can  be  effected  as  before,  by  means  of  an  analogous 
parallelepiped  —  in  this  case  triclinic,  however  —  whose  volume  is 
double  that  of  the  pseudo-hexagonal  space  unit. 


44  CHEMICAL  CRYSTALLOGRAPHY 

Since  the  introduction  of  topic  parameters  in  place  of 
the  crystallographic  axial  ratios  has  rendered  it  possible  to 
compare  with  one  another  the  corresponding  dimensions 
of  the  crystal  structures  of  different  substances,  we  may 
now  investigate  whether  in  certain  cases  the  change  in  the 
crystal  structure,  brought  about  by  a  chemical  change, 
takes  place  in  a  particular  direction,  so  that  conclusions 
might  be  drawn  therefrom  regarding  a  definite  mutual 
situation  of  the  atoms  in  the  crystal  structure.  Even 
from  a  comparison  merely  of  the  crystallographic  axial 
ratios,  it  had  previously  been  remarked1  that  often,  on 
the  substitution  of  hydrogen  by  some  other  univalent 
atom  or  radical,  an  alteration  takes  place  only  in  a  parti- 
cular direction  ;  this  phenomenon  was  called  morphotropy. 
At  the  same  time,  however,  it  remained  uncertain  whether 
the  apparent  increase  in  an  axial  ratio  was  not  in  reality 
due  to  a  diminution  of  the  other  two.  This  uncertainty 
disappears  on  comparing  the  topic  parameters  of  two  sub- 
stances, of  which  one  is  a  substitution  product  of  the 
other.  The  determination  of  the  topic  parameters,  how- 
ever, necessitates  very  accurate  determinations  of  the 
densities  of  the  crystallised  substances  which  are  to  be  com- 
pared, and  such  have  become  possible  only  in  recent  times  by 
the  improvement  of  methods,  and  especially  by  the  introduc- 
tion of  what  may  be  called  the  free  suspension  method, 
in  which  use  is  made  of  dense  liquids. 

That  this  method  is  the  only  one  applicable  to  the  accurate 
determination  of  the  densities  of  crystallised  substances,  was 
shown  by  Retgers.2  In  the  laboratory  of  the  author  it  has  been 
used  in  a  comprehensive  manner  by  Gossner  for  his  investigations, 
and  his  results  are  reproduced  in  the  following  paragraphs  : — 

The  nature  of  the  suspension  method  is  as  follows  :  By  suit- 
able admixture  of  two  liquids  a  third  is  obtained  having  the  same 

1  P.  Groth,  "Cber  Beziehungen  zwischen  Krystallform  und  chemischer 
Constitution  bei  eiuigen  organischen  Verbindungen,"  Berichtr  d.  d.  chem. 
G><.  1870,3,449. 

Chem.  1889,  3,  296  ;  Journ.  C.  S.  56,  812. 


MORPHOTROPY  45 

density  as  the  crystal  under  investigation,  as  shown  by  the  latter 
remaining  suspended  in  it,  neither  rising  nor  sinking.  The  density 
of  the  liquid  is  then  determined. 

Amongst  dense  liquids  which  are  suitable  for  this  purpose, 
when  employed  along  with  some  other  lighter  one,  there  may  be 
mentioned  : — 

1.  Acetylene  tetrabromide,  C2H2Br4.     D.  =  3-0x31  at  6°  C.    Can  be 
easily  prepared  by  passing  acetylene  into  cooled  bromine.1    Almost 
colourless,  and  very  stable  ;  easily  mobile. 

2.  Thoulet's    solution.      An    aqueous    solution    of   potassium 
mercuri-iodide  (KI  :  HgI2  in  the  ratio   I  :  1-239)  ;   introduced  by 
Thoulet,2  and  more  fully  investigated  by  V.  Goldschmidt.3     Almost 
colourless  ;  coefficient  of  expansion  small ;  hygroscopic  ;  somewhat 
viscous  ;  attacks  the  skin. 

3.  Methylene  iodide,  CH2I2.     D.  3-33.     Introduced  by  Brauns4 ; 
its  applicability  was  specially  brought  forward  by  Retgers.5    Nearly 
colourless  in  pure  state,  but  liable  to  decomposition  ;  easily  mobile  ; 
coefficient  of  expansion  very  large. 

4.  Klein's  solution.     An   aqueous   solution  of  cadmium  boro- 
tungstate,  2Cd(OH).2,B.2O3,9WO3,i6HoO.    D.,  up  to  3-28.     The  salt 
itself  melts  in  its  water  of  crystallisation  at  75°,  and  the  density 
of  the  liquid  thus  obtained  goes  up  to  3-6.6 

5.  Rohrbach's   solution.     An    aqueous    solution    of   100   parts 
barium  iodide  and  130  parts  mercuric  iodide.     D.,  up  to  3'588.7 

Only  the  first,  second,  and  third  of  these  liquids  are  employed 
for  chemico-crystallographical  investigations  ;  the  use  of  Klein's 
and  Rohrbach's  solutions  is  restricted  to  petrographical  work. 

Which  of  these  three  liquids  is  to  be  employed  depends 
naturally,  in  the  first  instance,  on  the  solubility  of  the  substance 
to  be  investigated.  Thoulet's  solution  is  diluted  with  water  ; 

1  Muthmann,  Zeits.f.  Kryst.  1899,  30,  73. 

2  Bull.  soc.  min.fr.  1879,  2,  17. 

3  N.  Jahrb.  f.  Min.  1 88 1,  Beil.-Bd.   I,   179;    Zeits.f.  Kryst.  7,  306; 
Journ.  C.  S.  44,  1 59. 

4  A',  fahrb.f.  Min.  1886,  2,  72. 

5  Zeits.f.  phys.  Chem.  1889,  3,  289  and  497  ;  Journ.  C.  S.  56,  812  and 

93L 

6D.  Klein,  Bull.  soc.  min.fr.  1881,  4,  149;  Zeits.f.  Kryst.  6,  306; 
Journ.  C.  S.  40,  1 1 68. 

7  Rohrbach,  Ann.  d.  Phys.  u.  Chemie,  N.  F.,  1883,  2O,  169;  Zeits.f. 
Kryst.  8,  422  ;  N.  Jahrb.  f.  Min.  1883,  2,  186  ;  Journ.  C.  S.  44,  1060. 


40  CHEMICAL  CRYSTALLOGRAPHY 

acetylene  tetrabromide  and  methylene  iodide,  with  benzene  or 
toluene,  less  satisfactorily  with  xylene. 

The  degree  of  accuracy  with  which  suspension  may  be 
arrived  at  depends  on  the  viscosity  of  the  liquid.  Thoulet's 
solution  is  somewhat^  viscous,  and,  further,  acts  on  the  human 
skin,  consequently  methylene  iodide,  or,  still  better,  acetylene  tetra- 
bromide, is  to  be  preferred  wherever  possible.  On  exposure  to 
light,  methylene  iodide  liberates  iodine  and  becomes  dark  coloured  ; 
it  also  acts  chemically  on  many  substances.  Acetylene  bromide, 
on  the  other  hand,  is  a  colourless  liquid,  which  requires  no 
purification  even  after  prolonged  use ;  as  additional  advantages 
are  to  be  reckoned  the  low  cost  and  the  convenient  method  of 
preparation.  It  seems  to  be  still  more  mobile  than  methylene 
iodide. 

As  regards  the  determination  of  the  density  of  the  suspending 
liquid,  the  method  described  by  Retgers i  is  not  very  convenient. 

The  following  method  is  rapid  and  accurate  to  a  few  units  in 
the  third  decimal  figure  : — The  liquid  is  prepared  in  a  test  tube, 
contact  with  the  hand  being  avoided  as  far  as  possible.  A  large 
number  of  the  purest  crystal  fragments  obtainable  are  introduced, 
and  the  densest  is  ultimately  brought  into  a  state  of  suspension. 
The  liquid  is  then  quickly  transferred  to  a  suitable  vessel,  and  its 
density  determined  by  means  of  an  accurate  Westphal  balance. 

The  temperature  of  the  liquid  is  here  of  no  moment,  provided 
it  is  the  same  in  the  mixing  and  measuring  vessels.  With  rapid 
working,  and  avoiding  unnecessary  contact  with  the  operator's 
hands,  this  condition  can  be  fulfilled  with  a  fair  degree  of  approxi- 
mation. 

It  is  necessary  to  state  the  temperature  at  which  the  density 
has  been  determined,  unless  it  is  to  be  tacitly  assumed  that  the 
experiment  was  carried  out  at  the  ordinary  laboratory  temper- 
ature of  I5°-2O°.  Retgers2  has  shown  that  with  temperature 
differences  amounting  to  io°-i5°,  the  variation  in  the  density 
may  already  exceed  the  observational  error. 

Although  a  very  short  period  has  elapsed  since  a 
beginning  was  made  with  the  determination,  by  the  fore- 
going method,  of  the  densities  of  substances  undergoing 
crystallographical  investigation,  and  consequently  the 

1  Zeits.f.phys.  Chem.  1889,  3,  289. 
:ts.  f.  phyv.  Chttn.  1889,  3,  307. 


MORPHOTROPY  47 

number  of  compounds  which  are  suitable  for  the  com- 
parison of  their  topic  parameters  is  still  very  limited,  there 
have  already  been  found  cases  in  which  substitution  has  pro- 
duced a  morphotropic  change  which  has  indubitably  taken 
place  in  a  particular  direction,  as  the  following  examples 
will  show  : — 

Ammonium  iodide  crystallises  in  cubes  exhibiting  perfect  cubic 
cleavage,  so  that  the  regular  space  lattice  constituting  the 
foundation  of  the  structure  must  be  the  simple  cubic  one.  Since 
the  density  (d}  of  the  crystals  is  2-501,  and  the  molecular  weight 
(M)  143-83,  the  equivalent  volume  V  is  57-51,  which  gives  3-860 
as  the  side  of  the  elementary  parallelepiped.  Slavik1  has  also 
investigated  the  compounds  in  which  the  four  atoms  of  hydrogen 
are  replaced  by  methyl,  ethyl,  and  propyl  groups.  Tetramethyl- 
ammonium  iodide  crystallises  tetragonally,  with  perfect  cleavage 
parallel  to  the  two  forms  {icoj  and  {ooij,  perpendicular  to  one 
another  ;  evidently,  therefore,  it  possesses  a  crystal  structure  which 
only  differs  essentially  from  that  of  ammonium  iodide  in  having 
the  dimensions  parallel  to  the  c  axis  different  from  those  parallel 
to  the  two  a  axes.  As  shown  in  the  table  below,  this  difference 
has  been  brought  about  by  a  lengthening  of  the  a  axes,  whilst 
the  value  of  w,  corresponding  to  the  c  axis,  has  undergone  no 
noteworthy  change.  Tetraethylammonium  iodide  also  cystallises 
tetragonally,  but  does  not  exhibit  the  complete  pseudo-cubic 
cleavage  of  the  methyl  compound ;  that  the  salt  nevertheless 
belongs  to  the  same  morphotropic  series  is  shown  by  the 
regular  progression  of  the  equivalent  volume  for  all  three  sub- 
stances, and  also  by  the  regular  increase  of  the  dimensions  x 
and  i/',  whilst  ^  has  again  undergone  only  slight  diminution. 
Hence  it  is  to  be  concluded  that  the  introduction  of  the  methyl 
and  ethyl  groups  into  the  crystal  structure  of  ammonium  iodide 
has  taken  place  in  one  of  the  three  cubic  planes  of  the  latter, 
which  plane  has  thereby  become  the  tetragonal  basal  plane, 
he  nitrogen  atoms,  for  example,  might  be  looked  upon  as 
occupying  the  centres  of  a  cubic  space  lattice  formed  of  iodine 
atoms,  the  hydrogen  atoms  being  arranged  between  them  on  the 
four  tetrahedron  face  normals  ;  the  carbon  and  hydrogen  atoms 
replacing  them  would  then  all  lie  in  a  horizontal  plane,  and 

1  Ztits.  f.  Kryst.  1902,  36,  268  el  seq. 


48  <  HKMIC.M.  CRYSTALLOGRAPHY 

this  would  necessitate  the  pushing  apart  of  the  iodine  atoms  in 
the  four  horizontal  directions.  If  still  larger  alkyl  groups  are 
introduced,  then  their  arrangement  in  a  plane  is  no  longer 
compatible  with  equilibrium,  and  there  results  an  arrangement  in 
space  which  leads  to  a  difference  in  the  two  horizontal  dimen- 
sions, and  to  a  considerable  pushing  apart  of  the  atoms  verti- 
cally. Hand  in  hand  with  this  there  is  an  alteration  in  the 
equivalent  volume,  which  no  longer  corresponds  to  that  between 
the  first  members  of  the  series.  (See  the  propyl  compound 
[rhombic]  in  the  table  below.) 


NH4I 

A 

N(CH3)4I 

A 

N<C,H.)41 

A 

N(C3H7)4I 

57-51 

51.19 

108-70 

54.21 

162-91 

73-04 

235-95 

3.860 

1.459 

5-3I9 

1.329 

6-648 

-0.555 

6-093 

3-  860 

1-459 

5-319 

1-329 

6-648 

1.103 

7-85I 

3-860 

-0.018 

3-842 

-0.156 

3-686 

1.247 

4-933 

Ammonium  chloroplatinate,  (NH4>j  PtCl«,  (cubic)  always  exhibits 
the  octahedron  as  its  predominating  crystal  form,  and  possesses 
perfect  cleavage  parallel  to  the  faces  of  that  form  ;  consequently, 
an  octahedral  structure  must  be  ascribed  to  it,  with  the  rhombic 
dodecahedron  for  the  shape  of  its  space  unit.  (See  page  42, 
No.  13.)  From  the  equivalent  volume,  V=  143-6,  it  follows  that 
the  side  of  the  corresponding  cube  (possessing  a  volume  four 
times  that  of  the  space  unit)  is  x  =  *f/  =  u  =  8-313-  Ifj  now,  one 
hydrogen  atom  in  each  NH4  is  replaced  by  methyl,  the  octa- 
hedron is  replaced  by  a  pronouncedly  pseudo-octahedral  form, 
constituted  by  a  rhombohedron  {in}  with  a  less  distinct  cleavage, 
and  a  very  perfect  cleavage  parallel  to  the  basal  pinacoid,  {in}  ; 
the  cube  of  ammonium  chloroplatinate  corresponds,  in  the  case 
of  methylammonium  chloroplatinate,  to  a  rhombohedron  {  100}, 
having  0  =  79°  5$'.  By  calculation  from  the  equivalent  volume, 
V=  186-5,  tne  s^e  of  this  rhombohedron  is  found  to  have  the 
value  x  =  ^  =  w  =  9«2i4.  Whilst,  therefore,  the  introduction  of  the 
two  methyl  groups  has  had  the  effect  of  causing  a  general 
pushing  asunder  of  the  atoms,  the  actual  linear  extension  has 
taken  place  along  one  only  of  the  four  trigonal  axes.  The 
deformation  therefore  corresponds  to  an  arrangement  of  the 
methyl  groups  in  one  of  the  four  trigonal  axes  of  the  structure 
of  the  ammonium  chloroplatinate.  It  is  therefore  to  be  expected 
that  the  substitution  of  all  four  hydrogen  atoms  of  the  ammonium 
radical  by  methyl  groups  should  induce  a  similar  expansion,  but 


MORPHOTROPY  49 

equally  so  in  all  four  of  the  trigonal  axes.  As  a  matter  of 
fact,  tetramethylammonium  chloroplatinate  is  again  cubic,  and 
crystallises  in  octahedra  with  perfect  octahedral  cleavage,  like 
the  ammonium  salt,  and  from  its  equivalent  volume,  ¥  =  304-4, 
the  value  x=$=w—  10-678  is  obtained.  That  the  space  dis- 
tribution of  the  methyl  groups  which  have  been  introduced  has 
taken  place  in  a  regularly  progressive  manner,  appears  from  a 
comparison  of  the  equivalent  volumes ;  for  the  increase  on 
passing  from  ammonium  chloroplatinate  to  the  monomethyl- 
ammonium  salt  is  approximately  one-fourth  of  that  on  passing 
from  the  former  to  the  tetramethylammonium  salt.  From  what 
has  just  been  stated  it  would  be  expected  that  the  replacement 
of  two  hydrogen  atoms  in  ammonium  by  methyl  groups  would 
lead  to  a  deformation  into  a  less  symmetrical  crystal  structure. 
As  a  matter  of  fact,  dimethylammonium  chloroplatinate  crystallises 
rhombic,  but  in  two  modifications,  only  one  of  which  possesses  an 
equivalent  volume  fitting  approximately  into  the  above  series  ; 
this  form  exhibits  cleavage  parallel  to  a  prism,  which  probably 
corresponds  to  that  cleavage  prism  of  the  ammonium  salt  which 
would  be  constituted  by  two  pairs  of  octahedral  faces.  On 
account  of  the  polymorphism  existing  in  this  case,  however,  a 
closer  comparison  cannot  be  carried  out  with  sufficient  proba- 
bility regarding  the  conclusions  drawn  ;  the  same  is  the  case  for 
the  trimethyl  compound. 

When  ethylammonium  chloroplatinate  is  compared  with 
ammonium  chloroplatinate,  it  becomes  evident  that  the  replace- 
ment of  one  atom  of  hydrogen  in  ammonium  by  an  ethyl 
group  gives  rise  to  the  production  of  an  essentially  different 
crystal  structure  ;  it  appears  from  the  properties  of  the  only 
known  modification  of  the  ethyl  compound  that  it  does  not 
represent  the  state  corresponding  to  the  above-mentioned 
methyl  compound.  The  crystals,  it  is  true,  are  apparently 
trigonal  with  a  very  perfect  cleavage  parallel  to  { 1 1 1 },  but  the 
other  faces  corresponding  to  those  of  the  octahedron,  namely, 
those  of  the  rhombohedron  {m},  are  never  observed  (nor  are 
they  on  the  isomorphous  bromoplatinate  nor  on  ethylammonium 
chlorostannate),  and  there  is  no  cleavage  parallel  to  them;  the 
observed  forms  point  rather  to  a  hexagonal  crystal  structure  (see 
page  43,  No.  14).  If  the  topic  parameters  of  ethylammonium 
chloroplatinate  are  calculated  in  accordance  with  this  assumption, 
we  obtain  :  V  =  217-93  x  =  t  =  6'546  w  ^  7-831. 

D 


50  CHEMICAL  CRYSTALLOGRAPHY 

This  modification,  which  consequently  does  not  correspond  to 
the  first  described  series  derived  from  ammonium  chloro- 
platinate,  undoubtedly  does  correspond  to  the  only  known  form 
of  propylammonium  chloroplatinate,1  whose  crystals,  though  mono- 
clinic,  nevertheless  possess  a  pronouncedly  pseudo-hexagonal  char- 
acter, with  perfect  cleavage  parallel  to  the  pseudo-hexagonal  basal 
plane.  If  the  dimensions  are  calculated  on  the  assumption  of  a 
pseudo-hexagonal  prism  (see  page  43)  as  the  space  unit  of  the 
crystal  structure,  with  its  basal  plane  making  an  angle  of  75°33*' 
with  the  front  prism  face,  then  the  following  values  are  obtained 
for  its  topic  parameters  : 

V  =  236-11     x  =  6-307     <A  =  6-528     w  -9-227. 

Isopropylammonium  chloroplatinate  belongs  doubtless  to  the 
same  morphotropic  series,  for  it  also  is  pronouncedly  pseudo- 
hexagonal,  with  basal  cleavage.  The  two  polymorphous  forms  of 
this  salt  mentioned  on  page  9  have  nearly  identical  angles,  and 
the  twinning  plane  of  the  lamella?  corresponds  to  a  face  of  the 
pseudo-hexagonal  prism.  The  topic  parameters  of  this  prism, 
whose  base  forms  right  angles  with  the  side  faces,  are  found  to 
be  as  follows  : 


V  =  234*95    X  =  6-3U    ^  =  6'585     w  =  8>829- 
Butylammonium   chloroplatinate,    which   exhibits   a    crystalline 
form  very  similar  to  the  preceding  one,  is  still  more  pronouncedly 
pseudo-hexagonal.     For  this  substance  the  analogous  calculation 
gives  the  values  : 

V  =  274-39    x  -  6<467    ^  =  6-623    u  =  9-945-'- 

Hence  it  is  evident  that  the  homologous  series  beginning 
with  the  ethylammonium  salt  forms  a  regular  morphotropic 

1  On  the  other  hand,  there  exists  a  second  modification  of  the  analogous 
chloro-t  -nnate,  trigonal  and  with  basal  cleavage,  whose  crystal  constants, 
however,  are  unknown  ;  if  this  modification,  in  the  case  of  pr<>pylammonium 
chloroplatinate,  were  obtainable  in  measurable  crystals,  it  would  doubtless 
prove  to  belong  to  the  morphotropic  series  first  described. 

3  The  data  regarding  the  substituted  ammonium  chloroplatinates  are 
derived  from  the  very  complete  investigations  of  J.  A.  Lc  Bel  and  A.  Ries 
(Ztit*.  /  A'rvst.  1902,  36,  321  el  seq.\  and  1904,  39,  49  et  seg.). 
By  these  authors,  however,  the  two  last-mentioned  salts  are  orientated  in 
a  manner  different  from  that  adopted  here,  the  pseudo-hexagonal  basal 
being  taken  as  |oioj. 


MORPHOTROPY  51 

series,  since  the  dimensions  of  the  hexagonal,  or  the  pseudo- 
hexagonal,  base  experience  only  insignificant  changes  by  the 
introduction  of  additional  methyl  groups,  whilst  the  height  of 
the  corresponding  prism,  which  constitutes  the  space  unit  of  the 
crystal  structure,  increases  about  equally  on  changing  from  ethyl 
to  propyl,  and  from  propyl  to  butyl.  This  would  therefore  indicate 
that  when  the  substitution  takes  place  these  groups  are  inserted 
in  the  direction  of  the  hexagonal  or  pseudo-hexagonal  axis  ;  in 
further  accordance  with  this  view  is  the  fact  that,  of  the  two 
propyl  derivatives,  it  is  the  one  which  has  the  shorter  carbon 
chain,  i.e.  the  isopropyl  compound,  which  exhibits  the  lower  value 
for -w. 

The  publications  of  Ries,  already  referred  to,  contain  still 
other  examples  of  this  kind  of  relationship.  Others  were 
supplied  by  the  investigation  of  G.  Mez  into  the  derivatives  of 
carbamide,1  from  which  what  follows  is  extracted  : — 

Carbamide  or  urea,  CO(NH2)>2,  crystallises  tetragonal,  and 
cleaves  very  perfectly  parallel  to  {no},  less  so  parallel  to  {ooi  j. 

Methylcarbamide  possesses  rhombic  symmetry,  but  exhibits 
an  exceedingly  perfect  cleavage  parallel  to  a  nearly  rectangular 
prism,  and  a  perfect  one  parallel  to  {ooij.  Hence  the  relation- 
ship between  the  crystal  structures  of  the  two  substances  is  so 
striking,  that  these  must  be  looked  upon  as  corresponding.  A 
comparison  of  their  topic  parameters  (see  the  following  table) 
shows  that  the  change  in  the  dimensions  is  restricted  essentially 
to  the  vertical  direction.  If  a  second  methyl  group  is  introduced 
on  the  same  nitrogen  atom,  there  results  as-dimethylcarbamide, 
whose  symmetry  is  monoclinic  and  which  exhibits  only  one 
perfect  cleavage.  Although  its  relationships  with  the  preceding 
compound  are  not  so  simple,  comparison  nevertheless  shows  that 
this  substitution  also  has  acted  in  a  similar  manner,  since  w  has 
still  further  increased,  whilst  x  and  ^  are  little  changed  (the 
mean  values  of  x  an^  <A  for  the  three  substances  are  respectively 
3778}  3-695,  and  3-581,  showing  a  regular  diminution). 


CO(NH;)2 

COXH2NHCH, 

•  "XH2N(CH.,), 

V  =    44.94. 

61-46 

7C-I2 

x  =     3-778 

3-676 

3.920 

y  «    3.778 

3713 

3.241 

w  =       3.148 

4.502 

5-531 

Zeits.f.  Kryst.  1902,  35,  242  et  seq. 


52  CHEMICAL  CRYSTALLOGRAPHY 

A  totally  different  morphotropic  effect,  resulting  from  the 
introduction  of  the  methyl  group,  is  observed  when  the  CH;; 
goes  to  the  second  nitrogen  atom  of  methyl  carbamide  or  of 
tfj-dimethylcarbamide  ;  though  the  crystals  of  the  two  derivatives 
thus  obtained,  respectively  rhombic  and  monoclinic,  also  have  two 
parameters  which  differ  but  little  from  one  another,  these  are  the 
two  larger  ones,  the  third  being  considerably  less. 

Metanitraniline  crystallises  rhombic  ;  if  its  predominating  prism 
is  taken  as  {  no},  then,  adopting  Schroder's  determination  of  the 
density,  we  obtain 

V  =  95-9    x  =  5-i8i     ^  =  3-479    »  =  5-3i8. 

By  introduction  of  a  methyl  group  this  substance  gives  rise  to 
i:2:4-nitrotoluidine,  for  which  Jaeger1  found  the  following  values  : 

V  =in-8    x  =  5-424    ^  =  3-882    w  =  5-670. 

Here  there  appears  to  have  taken  place  an  all-round  extension 
of  the  dimensions  of  the  crystal  structure  ;  actually,  however, 
the  deformation  has  proceeded  essentially  in  one  particular 
direction,  namely,  along  a  diagonal  of  the  plane  (oio)  of  the 
parallelepiped,  which  thereby  has  become  converted  into  a  mono- 
clinic  one. 

The  fact  that  in  many  cases  the  introduction  of  methyl 
for  hydrogen  brings  about  a  definitely  orientated  alteration 
of  the  crystal  structure,  results  in  the  crystals  of  homologous 
compounds  often  showing  a  similarity  in  the  angles  lying  in 
certain  zones.  This  phenomenon  has  attracted  attention 
for  some  considerable  time;  in  particular,  Hiortdahl2 
demonstrated  the  existence  of  a  series  of  such  cases,  and 
described  the  phenomenon  as  partial  isomorphism. 
Since  the  more  general  treatment  of  the  question  regarding 
the  alteration  brought  about  by  substitution,3  a  partial 
agreement  between  the  crystallographic  axial  ratios  of 
homologous  substances  has  been  proved  in  numerous 
examples.  Of  these  there  need  only  be  mentioned  the  two 
series,  derived,  the  one  from  formanilide,  C6H-NHCOH,  by 

1  Zeits.f.  Kryst.  1903,  38,  89. 
-Jour*,  prakt.  Chem.  1865,  94,  286. 
'1870,  Groth  loc.  cit. 


MORPHOTROPY  r>3 

replacement  of  the  hydrogen  of  the  COH  group  by  methyl, 
ethyl,  etc.,  the  other  from  acetanilide,  CGH5NHCOCH3, 
by  replacement  of  the  hydrogen  of  the  NH  group  by  alkyl 
radicals.  These  have  been  investigated  by  Wilson,1  but 
the  results  are  not  yet  published  in  detail. 

Experience  has  frequently  shown  that  the  introduction 
of  the  methyl  group  brings  about  an  alteration  of  the 
symmetry  of  the  crystal  structure  in  the  sense  of  diminish- 
ing, it,  as  has  already  been  shown  by  several  cases  among 
the  examples  given  above.  As  regards  the  extent  of  this 
change,  in  general,  we  should  expect,  a  priori^  that  it  must 
be  so  much  the  less,  the  more  preponderating  the  influence 
exercised  on  the  crystal  structure  by  the  remaining  con- 
stituents common  to  the  two  homologous  substances.  As 
a  matter  of  fact,  it  has  been  proved  by  numerous  examples 
that  the  morphotropic  effect  of  the  methyl  group  is  less>  the 
larger  the  chemical  molecule  of  the  compound  in  which  the 
substitution  is  carried  out.  How  slight  the  alteration  pro- 
duced by  the  introduction  of  the  methyl  group  may  be  in 
the  case  of  very  large  molecules  is  shown,  for  example,  by 
a  comparison  of  the  methyl  ester  of  phenaceturic  acid, 
Ct.H5.CH2.CO.NH.CH,.COOCH3,  with  the  ethyl  ester; 
both  possess  the  same  crystal  habit  and  nearly  identical 
angles.  Similar  behaviour  is  observed  with  the  esters  of 
naphthalene  sulphonic  acid,  C10H7SO3H,  santonic  acid,  and 
others,  in  which  the  difference  between  the  methyl  and 
the  ethyl  esters  is  generally  very  slight,  but  that  between 
the  acid  itself  and  the  methyl  ester  is  somewhat  greater. 

In  the  case  of  certain  substances  crystallising  in  the 
cubic  system,  no  change  whatever  appears  to  take  place 
on  the  substitution  of  methyl  for  hydrogen,  e.g.,  ammonium 
alum  and  trimethylammonium  alum,  ammonium  chloro- 
platinate  and  tetramethyl  ammonium  chloroplatinate.  It 
has  already  been  shown  on  page  48,  however,  that  although 
in  such  a  case  the  forms  of  the  crystals  coincide,  their 
structures  do  not,  for  the  dimensions  of  the  latter  ex- 
1  Rep,  Brit,  Assoc.  1900,  167, 


54  CHEMICAL  CRYSTALLOGRAPHY 

perience  a  considerable  increase  by  the  introduction  of  the 
methyl  groups.  On  this  account,  as  will  be  shown  later, 
two  such  homologous  substances  cannot  well  be  described 
as  isomorphous. 

It  is  therefore  evident  that  the  relations  between  the 
crystal  structures  of  substances  in  a  homologous  series  can 
be  recognised  only  by  a  comparison  of  the  dimensions  and 
angles  of  the  space  units  on  which  the  structures  are  based, 
and  for  this  the  requisite  complete  crystallographic  and 
volumenometric  investigations  (due  attention  being  paid  to 
the  question  of  polymorphism)  are  still  lacking  for  nearly 
all  homologous  series. 

The  same  considerations  apply  to  the  determination  of 
the  morphotropic  deformation  which  a  crystal  structure 
undergoes  on  the  introduction  of  a  halogen  atom  in  place 
of  a  hydrogen  atom.  Even  in  connection  with  the  first 
attempts  in  this  direction,  which  were  based  merely  on  the 
coincidence  of  the  angles  of  certain  zones,1  it  was  recognised 
that  the  morphotropic  effect  of  the  halogens  is  similar  to 
that  of  the  methyl  group,  and  consequently  the  halogen 
derivative  of  a  substance  possesses  in  many  cases  a  lower 
symmetry  than  the  substance  itself.  Quite  recently  it  has 
been  pointed  out  by  Jaeger2  that  this  analogy  is  determined 
by  the  agreement,  especially  between  Br  and  CH3,  as  regards 
the  way  in  which  they  occupy  space,  with  which  also  are 
connected  certain  analogies  in  the  chemical  behaviour  of  the 
respective  substances.  In  the  following  paragraphs  a  number 
<>f  examples  are  given  illustrative  of  the  morphotropic 
deformation  due  to  the  halogens:— 

i:2:4-Bromonitrophenol,  C6H3.OH.NO2.Br,  crystallises  mono- 
clinic,  and  possesses  the  following  topic  parameters : — 

107-87        x  =  8-6i2        1^  =  2.928        w=4-758        0=115°  56'. 
On  the  introduction   of  a    chlorine  atom   in   the   sixth   position 

1  Groth,  loc.  cit. 

.••./.  Mytt,  r.jo.|.  38,  5^7  tt  ^/, 


MORPHOTKOI'Y  55 

there  results  a  substance  which  also  crystallises  monoclinic  *  with 
the  parameters  : 

V=ii8-7o        x  =  6-204.        ^  =  5-926         (0  =  3.552        /3=ii4°38'. 

In  this  case  the  symmetry,  it  is  true,  has  not  been  lowered,  and 
£  has  retained  almost  the  same  value,  but  the  alteration  in  the 
structure  is  nevertheless  a  very  considerable  one,  since  the  value 
of  $  has  been  nearly  doubled,  while  those  of  x  and  u  have  been 
considerably  diminished. 

Acetanilide,  CoHsNHCoHaO,  at  ordinary  temperatures  possesses 
a  metastable  modification  (probably  monoclinic),  and  a  stable 
rhombic  modification  ;  so  also  does  p-chloracetanilide,  and  the 
two  stable  modifications  appear  to  represent  corresponding  states, 
since  they  possess  similar  cohesion,  in  accordance  with  which, 
therefore,  the  crystals  are  to  be  orientated.  This  gives  rise  to  the 
following  topic  parameters  (see  table),  which  show  that,  though  the 
symmetry  has  remained  unaffected  by  the  introduction  of  the 
chlorine  atom,  the  values  of  x  and  ^  have  undergone  a  considerable 
change  in  opposite  sense,  while  w  has  remained  nearly  unaffected. 
o-p-dichloracetanilide  according  to  Fels'  investigations2  is  mono- 
clinic,  so  that  here  the  diminution  of  symmetry  in  the  chemical 
molecule  is  associated  with  a  similar  change  in  the  crystal 
structure.  In  this  deformation  only  one  of  the  three  parameters, 
namely  x,  has  been  essentially  changed,  as  shown  by  the  following 
table  :— 

Acetanilide.  j>-Chloracetanilide.  o-p-Dichloracetanilidc. 

V     =      1  1  1-97  122.37  136-09 

X     =         8-260  6-825  8'259 


w  3-392  3-506  3.375 

It  would  be  interesting  to  continue  this  series  by  the  investiga- 
tion of  0-0-/-trichloracetanilide,  etc.  Of  those  substances  which 
are  derived  from  acetanilide  by  the  introduction  of  chlorine  into 
the  acetyl  group,  only  the  dichloro  compound  has  been  measured. 
It  crystallises  in  the  monoclinic  system,  but,  like  acetanilide, 
possesses  a  perfect  pinacoidal  cleavage  ;  if  this  is  here  also  taken 
as  {100},  then  the  predominating  form  becomes  {on},  with  an 
angle  of  80°  30',  whilst  the  corresponding  form  on  acetanilide 
would  have  an  angle  of  80°  28'  (calculated).  A  further  comparison 

1  Gossner,  Zeits.f.  Kryst.  1904,  40,  8  1. 
-  Zeits.  f.  Kryst.  1900,  32,  386,  407. 


56  CHEMICAL  CRYSTALLOGRAPHY 

is  impossible,  owing  to  the  lack  of  a  density  determination  for  the 
chlorine  compound. 

The  benzoic  acid  group  would  also  be  suitable  for  closer  study. 
The  crystals  of  this  acid  are  pronouncedly  pseudo-tetragonal,  with 
a  very  large  value  for  the  parameter  corresponding  to  the  tetragonal 
principal  axis,  and  it  is  rather  remarkable  that  no  cleavage  takes 
place  at  right  angles  to  this  axis.  Seeing  that  the  density  of  the 
measured  crystals  was  not  determined,  and  that  the  existing 
determinations  differ  very  greatly,  this  substance  certainly  requires 
further  investigation  as  regards  its  crystal  structure.  The  stable 
form  of  w -nitrobenzene  acid  has  retained  the  pseudo-tetragonal 
character  and  the  lack  of  cleavage  observed  with  benzoic  acid, 
but  possesses  a  much  shorter  principal  axis.  The  calculation  of 
the  topic  parameters  of  the  two  substances,  which  on  the  basis  of 
old  density  determinations  is  only  approximately  possible,  indicates 
(on  the  assumption  of  corresponding  conditions  of  structure)  that 
for  the  nitro-derivative  the  values  of  x  and  \f/  are  about  one  and  a 
half  times  as  large,  whilst  w  is  only  about  half  as  large,  as  for 
benzoic  acid.  Two  chloronitrobenzoic  acids  are  formed  from  the 
above-mentioned  nitrobenzoic  acid ;  these  have  been  investigated 
by  Jaeger,1  and  their  topic  parameters  are  : 

(\!I;C1.NO,,.COOH  x  =  3-i67  ^  =  2-765  W=i6.62o 

4       1  =  3        1 

CgHjCl.XOo.COOH  x  =  5-I48  ^  =  4-022  u=  6-925. 

The  typically  pseudo-tetragonal  crystals  of  the  2  :  5  acid  have 
nearly  the  same  values  of  x  and  ^  as  benzoic  acid  has,  but  have 
a  still  larger  value  for  a>,  and  correspondingly  complete  cleavage 
on  {ooi[  ;  compared  with  nitrobenzoic  acid,  they  exhibit  diminu- 
tion of  x  and  \f,  and  very  marked  increase  of  w.  The  4  :  5  acid  shows 
greater  similarity  of  habit  with  nitrobenzoic  acid,  and  differs  from 
it  in  that  x  and,  more  especially,  w  have  undergone  a  not  incon- 
siderable increase,  whilst  ^  has  experienced  a  slight  diminution. 
The  same  observer  has  also  investigated  two  isomeric  chloro- 
benzoic  acids,  and  found  for  them  : 

Cl.COOH  :-638  ^  =  8.508  w  =  2-ii8 

C6H4C1.COOH  *  =  3-697  ^  =  2-902  w  =  9-662 

In  both  of  these  pairs  of  cases  it  is  evident  that  the  morphn- 
1  /.fit!./.  Am/.  1903,  38,  301, 


MORPHOTROPY  57 

tropic  effect  of  chlorine  is  entirely  different  when  it  takes  up 
different  positions  in  the  molecule  ;  and  it  is  found  generally  that 
two  (position-}  isotneric  derivatives  of  benzene  possess  essentially 
different  crystal  structures. 

An  apparent  exception  to  this  rule  has  been  found  by  Jaeger ! 
in  the  case  of  the  1:2:4:6.-  and  1:2:3:  5-tribromotoluenes,  whose 
crystalline  forms  and  equivalent  volumes  are  as  closely  similar  as 
in  the  case  of  isomorphous  substances.  Since  the  dibromotoluenes 
(mostly  liquids)  have  not  been  crystallographically  determined, 
no  evidence  can  be  adduced  as  to  how  this  relationship  might  be 
explained  by  the  change  produced  in  the  crystal  structure  of  the 
dibromo  compounds  by  the  introduction  of  a  third  bromine  atom. 

Coincidence  of  the  angles  lying  in  certain  zones  is  shown 
by  m-nitroacetanilide  and  p-bromo-w-nitroacetanilide,  likewise  by 
p-nitroacetanilide  and  certain  of  its  halogen  derivatives,  but  the 
available  data  are  too  incomplete  to  allow  of  regularities  being 
recognised.  Further  interesting  series  would  be  supplied  by  the 
halogen  derivatives  of  methyl-p-tolylsulphone,2  which  in  part  show 
very  close  relationships  between  their  crystalline  forms  ;  also,  the 
chloro  and  bromo  substitution  compounds  of  naphthalene  tetra- 
chloride,  whose  angles,  according  to  the  investigations  of  Hintze,:! 
generally  display  very  considerable  similarities. 

The  observations  so  far  recorded  uniformly  indicate  that 
the  morphotropic  effect  of  the  halogens  possesses  certain 
analogies  with  that  of  methyl,  and  that,  like  the  latter, 
it  becomes  less  evident  the  larger  and  more  complex  the 
chemical  molecule  in  which  the  substitution  occurs. 

The  similarity  of  the  effect  of  chlorine,  bromine,  and 
iodine,  on  which  the  isomorphism  of  the  halogen  com- 
pounds depends,  will  be  discussed  later. 

It  appeared  from  numerous  examples  of  aromatic  sub- 
stances4 that  the  morphotropic  effect  of  the  nitro-group  is 
less  than  that  of  methyl  or  the  halogens,  and  consequently 
that,  in  cases  where  different  states  due  to  polymorphism 
are  not  involved,  the  close  relationship  of  the  nitro- 

1  Loc.  cit.,  p.  577. 

-  See  Zeits.f.  Kryst.  1892,  2O,  604. 

:!  Poggend,  Ann.  d.  Phys.  1874,  Erg.-Bd.  6,  177. 

4  Groth,  he.  cit. 


58  CHEMICAL  CRYSTALLOGBAPHY 

derivatives  to  the  parent  substance  can  be  recognised 
immediately  from  the  coincidence  of  the  angles  in  a 
principal  zone,  *'.<?.,  from  the  similarity  of  the  ratios  of  two 
of  the  crystallographic  axes.  On  that  account  these 
relationships  could  even  be  employed  for  the  purpose  of 
drawing  conclusions  of  a  chemical  nature.  In  the  year 
1876  Hepp  prepared  a  trinitrobenzene  which  was  crystallo- 
graphically  examined  by  Friedlander,1  when  it  was  found 
that  the  compound  exhibits  morphotropic  relationships,  of 
the  kind  here  referred  to,  with  meta-dinitrobenzene,  but  not 
with  either  ortho-  or  para-dinitrobenzene ;  its  nitro- 
groups  must  consequently  occupy  the  positions  1.3.5,  an^ 
the  correctness  of  this  conclusion  has  since  been  amply 
confirmed  in  other  ways.  These,  and  the  other  investigations 
on  the  nitro-derivatives  of  benzene  and  of  phenol,  and  of 
their  halogen  substitution  products,  still  require  much  sup- 
plementary work,  however,  and  especially  the  provision  of 
density  determinations  (which  are  almost  entirely  lacking) 
before  the  establishment  of  quantitative  regularities  will  be 
rendered  possible.  Professor  Korner,  in  Milan,  to  whom 
especially,  as  is  well  known,  we  owe  the  correct  deter- 
mination of  the  positions  in  these  benzene  derivatives,  is 
engaged  upon  a  comprehensive  revision  of  this  group  of 
substances,  simultaneously  with  which  the  complete  crystal- 
lographical  determination  of  the  compounds  will  be  carried 
on,  so  that  we  may  expect  to  see,  before  very  long, 
important  advances  in  the  recognition  of  the  relations 
between  crystal  form  and  chemical  constitution  in  the  case 
of  benzene  derivatives.  On  that  account,  only  a  few 
examples  will  be  mentioned  in  what  follows,  to  illustrate 
the  morphotropic  role  which  is  played  by  the  nitro-group. 

Whilst  in  many  cases  the  crystal  symmetry  is  not  altered  by 
the  substitution  of  the  nitro-group  for  hydrogen,  in  other  cases  it  is 
lowered,  especially  when  the  symmetry  of  the  chemical  molecule  is 
similarly  affected.  Such  is  the  case,  for  example,  with  the  mono- 
clinic  p-dibromobenzene  ;  this,  on  the  introduction  of  a  nitro-group, 
1  '/.tin.  f.  AVw/.  1879,  3,  1 68, 


MORPHOTROPV  59 

gives  rise  to  a  triclinic  form  whose  prism  zone,  however,  possesses 
almost  exactly  the  same  angles  as  the  prism  zone  of  the  original 
substance. 

An  illustration  of  the  symmetry  of  the  crystal  structure  remain- 
ing unchanged  when  the  symmetry  of  the  chemical  molecule  also 
remains  as  before,  is  provided  by  acetanilide  and  p-nitroacetanilide, 
which  both  crystallise  in  the  rhombic  system.  As  we  have  here  to 
deal  with  somewhat  large  chemical  molecules,  the  entrance  of  the 
nitro-group  effects  only  a  moderate  change,  so  that,  when  the  two 
substances  are  so  orientated  as  to  have  their  pronounced  cleavages 
coincident,  their  crystallographic  axial  ratios  become  very  similar, 
especially  if  the  predominating  prism  on  acetanilide  is  taken 
as  fnoj  : 

C6H5.NH.C2H,O  <i:  Arc  =1-0335  :  I  :  0-8421 

C6H4NO, .  NH  .  C2H3O  1-0445  :  I  :  0-8889. 

When,  on  the  other  hand,  the  nitro-group  takes  up  the  less 
symmetrical  meta  position  in  acetanilide,  the  symmetry  of  the 
crystal  structure  becomes  monoclinic  ;  nevertheless,  its  relation  to 
that  of  acetanilide  remains  a  very  intimate  one,  for,  assuming  the 
perfect  cleavage  here  to  be  orientated  in  the  same  way  as  the  plane  of 
perfect  cleavage  in  acetanilide,  jioo],  the  bipyramidal  combination 
!mj  {ill}  of  the  nitro-derivative  represents  simply  the  rhombic 
pyramid,  occurring  on  the  other  substance,  deformed  into  a  mono- 
clinic  one  ;  i.e.,  if,  inversely,  that  monoclinic  combination  were 
subjected  to  a  homogeneous  deformation  such  that  it  attained 
rhombic  symmetry,  there  would  then  result  a  form  with  angles  very 
similar  to  those  exhibited  by  the  solitary  bipyramid  observed  on 
acetanilide. 

The  series  of  nitrobenzoic  acids  is  more  completely  known — 
not  their  densities,  however.  From  a  comparison  of  the  following 
crystallographic  axial  ratios 

C6H5.COOH  <?  :<5:c=  1-0508:  i  :4-2o84         £  =  97°     5' 

4  1 

C2H4.NO2.COOH  2-5432:1:4-2349  96    42$ 

it  appears  probable  that  by  the  entrance  of  a  nitro-group  into  the 
para  position,  whereby  the  symmetry  has  not  been  affected,  a 
change  has  taken  place  only  along  the  direction  of  the  a  axis. 
The  morphotropic  effect  of  the  nitro-group  is  quite  different,  how- 
ever, when  this  takes  up  either  of  the  other  positions,  whereby  the 


60  CHEMICAL  CRYSTALLOGRAPHY 

symmetry  of  the  chemical  molecule  also  is  diminished.  Ortho- 
nitrobenzoic  acid  is  triclinic,  and  forms  tabular  crystals  whose  pre- 
dominating lateral  faces  make  an  angle  of  69°  o'  with  the  tabular 
face  (a  :  by  according  to  Haushofer),  whilst  the  corresponding  angle 
(c :  /)  of  benzoic  acid  is  69°  24'.  (The  comparison  cannot  be  carried 
further,  because  the  elements  of  0-nitrobenzoic  acid  are  not  com- 
pletely known).  Metanitrobenzoic  acid,  according  to  Bodewig, 
exists  in  three  modifications,  of  which  the  stable  one  has  a_prism 
angle  of  87°  48',  whilst  for  benzoic  acid  the  angle  (no):  (no)  is 
87°  36' ;  both  substances  are  monoclinic,  but  an  alteration  in  the 
symmetry  has  taken  place  here  also,  for  the  form  [ooij,  which  pre- 
dominates in  each  case,  is  in  the  one  inclined  in  the  plane  (oio), 
and  in  the  other  in  the  planes  (100).  Of  the  dinitrobenzoic  acids, 

2.4  1 

the  compound  C6H:5(NO2)o.  COOH  is  known  in  two  modifications, 
of  which  the  stable  one  exhibits  an  unmistakable  relation  to 
paranitrobenzoic  acid;  both  possess  perfect  cleavage  on  -jioij, 
the  angle  /3  amounts  to  96°  42^'  and  97°  21'  respectively,  and  the 
ratio  a :  c  is  likewise  similar  in  both  cases,  so  that  the  alteration 
due  to  the  entrance  of  the  second  nitro-group  seems  to  be  confined 
essentially  to  the  axis  b.  Owing  to  our  incomplete  knowledge 
of  orthonitrobenzoic  acid,  the  relations  of  the  dinitro  acid  to  it 
cannot  be  determined.  On  the  other  hand,  those  of  the  acid 

i 

C6H;,(NO2).>.  COOH  to  metanitrobenzoic  acid  (the  only  mononitro 
acid  from  which  the  former  can  be  derived  by  introduction  of  the 
nitro-group)  are  very  distinct :  habit  and  cleavage  are  the  same 
in  the  two  substances,  and  the  axial  ratios  : 

Metanitrobenzoic  acid  a  :/>:  c- 0-9656  :  I  :  1-2327         ft  =  91°  II' 

Metadinitrobenzoic  acid  1.1191  :  I  :  1*1294  96°  23. 

show  that  the  morphotropic  effect  is  now  no  longer  a  very  pro- 
nounced one.  If,  finally,  the  two  nitro-groups  are  introduced  into 
the  benzoic  acid  molecule  so  that  they  replace  the  two  hydrogen 
atoms  neighbouring  to  the  carboxyl  group,  then  the  crystalline 
form  of  the  acid  becomes  rhombic  with  the  axial  ratios  a  \b\c~ 
0.817  :  I  -'2.305,  whilst  the  habit  of  the  crystals  exhibits  the  greatest 
similarity  with  orthonitrobenzoic  acid  and  benzoic  acid  itself. 

Trinitrobenzoic  acid,  C,,I  I,(NO2)3.  COOH,  possesses  the  same 
symmetry  as  the  preceding  compound  ;  it  crystallises  rhombic, 


MORPHOTROPY  61 

with  the  axial  ratios  a  :  b :  £-  =  0-8757  :  I  :  0-5005,  and  its  pre- 
dominating prism  {101}  exhibits  angles  similar  to  those  of  the 
corresponding  faces  (101)  and  (101)  of  paranitro-benzoic 
acid. 

An  example  illustrating  that  with  still  larger  chemical  mole- 
cules the  change  caused  by  the  entrance  of  the  nitro-group 
becomes  still  less  marked,  is  supplied  by  the  nearly  complete  coin- 
cidence of  crystal  structure  shown  by  tri-  and  tetra-nitro-p- 
azotoluene.1 

For  a  study  of  the  morphotropic  effect  of  the  amido- 
group  there  does  not  at  present  exist  any  sufficient  material 
in  the  form  of  crystallographical  investigation. 

As  regards  the  hydroxyl  group,  on  the  other  hand,  it 
was  pointed  out  by  the  author,  as  far  back  as  1870,  that  its 
introduction  into  benzene  in  the  place  of  the  hydrogen  did 
not  affect  the  symmetry,  and  modified  the  dimensions  only 
in  one  particular  direction.  As  a  matter  of  fact,  investiga- 
tions instituted  since  then  have  shown  that  the  morpho- 
tropic effect  of  hydroxyl  in  aromatic  compounds  presents 
certain  analogies  with  that  produced  by  the  nitro-group. 
A  few  examples  may  serve  to  illustrate  the  relationships 
arising  in  connection  with  this  substitution. 

A  comparison  may  be  made  between  w-dinitrobenzene  and  two 
dinitrophenols  derived  from  it  by  the  introduction  of  hydroxyl : 


1  •  3 


C6H4(NOo).j  rhombic          a:6:  c  =  0-2855  :  I  :  0-5302 

C6H3(N02)2 .  OH  „  0-4487  :  i  :  0-5278 

1.3  4 

C6H3(NOo).j.OH     monoclinic  0-2972:1:0-5552     /3=lo6°2o' 

In  the  one  case,  therefore,  there  is  retention  of  the  symmetry, 
and  alteration  along  one  axis,  and  in  the  other  case  the  axial  ratios 
remain  almost  unaffected  whilst  a  lower  symmetry  results  from  the 
deformation.  Here,  in  the  meantime,  only  the  relative  changes 
can  be  determined,  but  in  the  following  example  it  is  possible  to 
determine  the  topic  parameters  themselves. 

1  Zepharovich,  Zeits.f.  Kryst.  1889,  15,  218. 


<V3  CHEMICAL  CRYSTALLOGRAPHY 

The  symmetrical  trinitrobenzene  mentioned  on  page  58  has 
recently  been  more  fully  investigated  by  Peruzzi  in  the  laboratory 
of  the  author,  on  material  obtained  by  Koerner,  as  has  also  the 
symmetrical  trinitrophenol  (picric  acid),  which  has  already  been 
repeatedly  measured  ;  and  accurate  density  determinations  of  both 
have  been  carried  out  by  Gossner.  By  means  of  crystallisations 
rich  in  faces,  obtained  at  different  temperatures  and  from  different 
solvents,  the  fundamental  form  of  both  of  these  substances,  which 
crystallise  rhombic,  could  be  deduced  with  a  great  degree  of 
probability. 

The  following  values  were  obtained  : — 

I  .  :; . .", 

C6H3(NO«):,  V=i25-3i        x=S'274        t  =  $-66$        w  =  4-n6 

1.3.  S 

C6H._,(NO2),.OH  128-41  4-917  5-074  5-147. 

A  comparison  of  these  shows  that  the  deformation  consists  in  a 
marked  increase  of  w,  combined  with  a  slight  contraction  in  the 
directions  of  x  and  ^. 

Still  less  marked  are  the  changes  which  are  brought  about  by 
the  introduction  of  the  hydroxyl  group  into  the  benzoic  acid  mole- 
cule, with  formation  of  salicylic  acid  ;  and  also  into  that  of  w-nitro- 
benzoic  acid  with  formation  of  the  acid 

C6H3.UH.NO2.COOH. 

In  both  cases  we  have  to  deal  with  monoclinic  substances  whose 
crystal  symmetry  is  not  changed  by  the  substitution  ;  in  the  first 
case  there  is  a  dimensional  alteration,  but  only  in  one  direction  ; 
in  the  second  case  there  are,  all  over,  only  relatively  small  altera- 
tions. 

Naphthalene,  C10H8,  crystallises  monoclinic,  as  do  also  a-  and 
/3-naphthol,  C,0H7OH  ;  both  isomers  possess  a  crystal  habit  coin- 
ciding with  that  of  naphthalene,  and  the  angles  of  all  three  are  so 
much  alike  that  they  have  been  stated  to  be  "isomorphous." 

The  results  of  the  very  incomplete  investigations  so  far 
made  regarding  the  influence  which  the  substitution  of 
hydrogen  by  methyl,  chlorine,  bromine,  iodine,  the  nitro- 
group,  and  hydroxyl,  exercises  on  the  crystal  structure,  may 
be  summed  up  in  the  following  statements  : — 


MORPHOTROPY  63 

///  many  cases  the  alteration  demonstrably  takes  place  in 
definite  directions,  so  that  it  is  possible  to  draw  therefrom 
conclusions  regarding  the  arrangement  of  the  atoms  in  the 
regular  structure. 

The  nature  and  extent  of  the  deformation  depend  not  only 
on  the  nature  of  the  substituting  constituent  (atom  or  radical), 
and  on  the  crystal  structure  of  the  substance  in  which  the 
substitution  takes  place,  but  also  : 

1 .  On  the  position  occupied  by  the  replaced  hydrogen  atom 
in   the   chemical  molecule   (consequently  isomeric  substances 
possess  different  crystal  structure]  ;  and 

2.  On  the  size  of  the  chemical  molecule,  since  the  altera- 
tion of  the  crystal  structure  in  general  becomes  less,  the  more 
complex  the  composition  of  the  compound  in  which  the  chemical 
change  under  consideration  takes  place. 

Similar  relationships  are  recognisable  on  comparing  the 
crystallographical  properties  of  acids  and  those  of  their  salts, 
which  would  indicate  that  the  morphotropic  effect  of  metals, 
on  their  introduction  into  the  molecule  of  the  acid  in  place 
of  hydrogen,  is  subject  to  similar  regularities.  Since  the 
majority  of  inorganic  acids  cannot  be  subjected  to  crystallo- 
graphical investigation,  such  comparisons  can  be  undertaken 
almost  exclusively  with  organic  acids,  and  even  with  these 
there  is  often  no  direct  relationship  observable,  evidently 
because  in  such  cases  the  change  produced  by  the  substitu- 
tion is  too  radical  a  one.  Here  again,  the  relationships  are 
much  more  distinctly  recognisable  in  the  case  of  the 
benzene  derivatives,  especially  with  the  potassium  and 
ammonium  salts  of  the  more  complicated  aromatic  acids, 
amongst  which  there  occur  many  stable  substances  which 
crystallise  in  the  anhydrous  state,  and  so  are  suitable 
for  comparison.  Since  the  present  problem  has  as  yet  been 
the  subject  of  no  systematic  treatment,  it  is  in  the  meantime 
possible  to  give  only  such  isolated  examples  as  have  been 


64  CHEMICAL  CRYSTALLOGRAPHY 

discovered  more  or  less  accidentally  in  the  course  of 
crystallographical  investigations. 

According  to  Fock,  amidosulphonic  acid,  NH2SO3H,  crystal- 
lises rhombic,  as  does  also  its  potassium  salt ;  the  following  are 
their  axial  ratios,  and  it  will  be  observed  that  a  and  b  exhibit  a 
striking  agreement : 

NHoSOgH  a:&:  t  =  0-9948  :  I  :  i'H«7 

NH2SO3K  0-9944  :  i  :  0-7097. 

In  the  case  of  tartaric  acid  and  its  ammonium  salt  (the  latter 
investigated  by  WyroubofT),  determinations  of  the  densities  are 
available,  so  that  their  topic  parameters  can  be  given  ;  they  both 
crystallise  monoclinic  : 

V  x  t  "  ft 

(CH.OHXCOOH).,  84-52      5-142      4-034      4-'4i       79°  43' 

(CH.OH)JCOONH4),      114-17      4-727      4-113       5-878      87°  35- 

The  deformation,  therefore,  consists  essentially  in  an  increase 
in  w. 

Glutamic  acid  crystallises  rhombic,  its  acid  sodium  salt  mono- 
clinic,  but  both  exhibit  a  very  closely  agreeing  ratio  b  \c  : 

COOH(CHo)2.  CHNHo.  COOH       a  :  b  :  c  =  o-687  :  i  :  0-855 
COOH(CH2)2.CHXH2.COONa  1-013:1  :  0-864     £  =  97°  59'. 

With  picric  acid  and  its  potassium  salt,  which  both  crystallise 
rhombic,  the  dimensions  of  the  space  units  can  be  directly  com- 
pared ;  they  are  : 

C6H2(NO.,)3OH  V  =  128-41  *  =  4-9i7  ^  =  5-o74  ^  =  5'i47 
C6H2(N02)3OK  144-43  6-521  4-548  4-868. 

The  deformation  due  to  the  entrance  of  the  potassium  atom 
consists,  therefore,  in  a  considerable  dilation  in  the  direction  of  x> 
and  a  slight  contraction  in  the  plane  at  right  angles  thereto.  This 
somewhat  stable  plane  is  simultaneously  the  one  parallel  to  which 
the  crystals  of  both  substances  generally  exhibit  tabular  develop- 
ment. From  this  it  may  be  assumed  with  considerable  probability 
that,  in  the  space  unit  of  the  crystallised  acid,  the  hydroxyl 
occupies  such  a  position  that  the  potassium  atom  entering  in  place 
of  hydrogen  must  produce  a  pushing  asunder  of  the  remaining 
atoms  in  the  direction  normal  to  that  plane. 

Similar  relationships  seem  to  exist  between  benzoic  acid  and 
phenylglycollic  acid  on  the  one  hand  and  their  ammonium  salts  on 


MORPHOTROPY  65 

the  other,  but  these  cases  require  fuller  investigation.  The  same 
remark  applies  to  phthalic  acid  and  the  acid  sodium  phthalate, 
which  exhibit  a  very  great  similarity  in  their  axial  ratios,  so  that, 
corresponding  to  the  large  size  of  the  chemical  molecule,  the 
entrance  of  the  sodium  can  have  caused  only  a  moderate  alteration 
in  the  dimensions  of  the  crystal  structure. 


E 


ISOMORPHISM 

A.    Similarity   of   Crystal   Structure  in  Substances 
possessing  Analogous  Chemical  Constitution 

AT  the  end  of  the  previous  section  attention  was  called  to 
the  fact  that,  as  regards  crystal  structure,  the  sodium  salt  of 
phlhalic  acid  exhibits  an  intimate  relationship  with  the  acid 
itself.  The  corresponding  salts  of  potassium,  rubidium, 
caesium,  and  ammonium  crystallise  very  like  the  sodium 
salt,  and  it  is  therefore  to  be  assumed  that  the  alteration  in 
the  crystal  structure  of  phthalic  acid,  which  results  from  the 
substitution  of  one  or  other  of  the  above  metals  for  hydro- 
gen, in  each  case  takes  place  in  the  same  direction  and  is 
similar  in  extent  ;  on  this  ground,  therefore,  the  analogously 
constituted  salts  of  these  metals  must  possess  crystal 
structures  whose  space  units  are  characterised  not  only 
by  like  symmetry,  but  also  by  nearly  the  same  linear 
dimensions  and,  consequently,  nearly  the  same  volume. 
For  this  it  is  evidently  necessary  that,  in  the  first  place, 
the  elements  concerned  should  be  capable  of  playing  an 
analogous  role  in  the  chemical  molecule,  and  this,  as  a 
matter  of  fact,  is  the  case  with  the  above-mentioned  metals 
and  ammonium.  The  differences  in  the  dimensions  of  the 
space  units  of  the  individual  salts  of  such  a  series,  being 
brought  about  by  the  lack  of  equality  in  the  space  occupied 
by  the  atoms  of  the  different  metals  in  the  crystal  structure, 

60  ' 


ISOMORPHISM  67 

must,  therefore,  appear  most  marked  in  that  direction  in 
which  the  principal  alteration  of  the  crystal  structure  of  the 
acid  takes  place.  If,  now,  we  compare  the  crystallographic 
axial  ratios  of  the  phthalates  of  sodium,  potassium, 
rubidium,  caesium,  and  ammonium,  we  find  not  inconsider- 
able differences  in  the  values  of  a  and  c  (b  being  taken  as 
unity),  while  the  ratio  a  :  c  differs  only  slightly  in  the  differ- 
ent members  of  the  group.  It  is,  therefore,  to  be  presumed 
that  the  former  differences  depend  on  corresponding  differ- 
ences in  the  value  ^  (corresponding  to  b\  and  that  it  is  in 
this  direction  that  the  principal  deformation  of  the  crystal 
structure  of  the  acid  takes  place  on  the  introduction  of  the 
metals  under  consideration. 

This  is  in  agreement  with  the  fact  that,  in  the  case  of 
the  rubidium  and  caesium  salts,  whose  densities  are  known, 
the  greatest  difference  in  the  topic  parameters  is  that  affect- 
ing the  value  of  ^,  corresponding  to  the  b  axis. 

The  1 12  :4-bromonitropheriol  mentioned  on  page  54  pro- 
vides a  case  where  the  relations  which  the  crystal  structures 
of  several  analogous  derivatives  bear  to  the  crystal  structure 
of  the  substance  from  which  they  are  jointly  derived,  can  be 
directly  recognised  by  a  comparison  of  the  topic  parameters. 
In  this  crystal  structure  the  introduction  of  chlorine  into 
the  sixth  position  produced  the  greatest  change  in  the  value 
of  ^,  and  the  least  in  the  value  of  w  ;  bromine  and  iodine 
behave  in  an  entirely  analogous  manner  when  they  replace 
the  same  hydrogen  atom  (6),  as  is  evidenced  by  the  follow- 
ing table  of  the  topic  parameters  of  the  three  substances 
(according  to  Gossner's  investigation l)  : — 

1  2  4         6  V  X  t  <"  ft 

C6H2.OH.XO.2.Br.Cl  1187  6-204  5.926  3-552  114°  38' 
C6H2.OH.NO2.Br.Br  121-1  6-207  6-025  3-562  114  37 
C6H2.OH.NO2.Br.I  129-0  6-413  6-167  3-578  114  14 

When  these  values  are  compared  it  is  seen  that  the 
greatest  difference  (percentage  as  well  as  actual)  occurs  with 

1  Loc.  cit. 


68  CHEMICAL  CRYSTALLOGRAPHY 

^,  and  the  least  with  w  ;  i.e.,  those  directions  in  which 
respectively  the  greatest  and  the  least  change  results  in  the 
crystal  structure  of  bromonitrophenol  when  a  halogen  atom 
is  introduced  in  place  of  hydrogen  (see  page  55).  The  three 
analogous  derivatives  form  a  progressive  series  as  regards 
the  habit  of  their  crystalline  form  and  the  dimensions  of 
their  space  units,  so  that  here  a  higher  atomic  weight  for 
the  substituting  element  carries  with  it  the  occupation  of  a 
greater  space  as  measured  in  all  three  directions. 

Such  a  series,  progressing  with  the  atomic  weight  of  the 
substituents,  may  often  be  recognised  merely  on  comparison 
of  the  angles,  as  in  the  cases  of  the  chloro-  and  bromo- 
derivatives  of  hydroquinone  and  of  phenylpropionic  acid.1 
Here  again,  however,  demonstration  of  the  prevailing  regu- 
larities is  placed  beyond  doubt  only  by  a  comparison  of  the 
topic  parameters,  for  which  purpose  these  were  first  intro- 
duced (see  page  38). 

The  most  comprehensive  and  exact  investigations  of 
such  series  of  analogously  constituted  and  similarly  crystal- 
lised substances,  are  those  of  A.  E.  Tutton  on  the  normal 
sulphates  of  potassium,  rubidium,  and  caesium,2  the  cor- 
responding selenates,3  and  the  double  sulphates  and 
selenates  of  these  univalent  metals  with  bivalent  ones.4 

By  these  masterly  researches  the  proof  has  been 
supplied  that,  in  the  salts  named,  the  replacement  of  potas- 
sium by  rubidium,  and  of  this  by  caesium,  brings  about  a 
change  in  the  geometrical  and  physical  properties  of  the 
respective  crystals,  which  change  progresses  with  the  atomic 
weights  of  the  metals,  so  that  in  the  case  of  the  rubidium 
salt  the  value  for  any  property  always  lies  between  the 
values  for  the  same  property  in  the  corresponding  potassium 
and  caesium  salts.  The  following  table  contains  the  dimen- 

1  FeU,  Zeits.f.  Kryst.  1900,  32,  396-8. 

"tjourn.  C.  S.  1894,  65,  628  ;  1896,  69,  495  ;  Zeits.f.  Kryst.  24,  I ;  37,  252. 
*Journ.  C.  S.  1897,  71,  846  ;  Zeits.f.  A'ryst.  29,  63. 
4Journ.  C.  S.  1893,  63,  337;  1896,69,  344;  Proc.  Roy.  Soc.  1900,  66, 
248  ;  1901,  68,  322  ;  Zeits.J.  Kryst.  21,  491  ;  27,  113,  33,  I  ;  35,  529. 


ISOMORPHISM  69 

sions  of  the  space  units  for  the  normal  sulphates  and  selen- 
ates,  the  crystal  structure  being  referred  to  a  rhombic  space 
lattice,  which,  however,  differs  extraordinarily  little  from  a 
hexagonal  one  ;  the  space  unit  is  here  taken  as  a  pseudo"- 
hexagonal  prism  (see  page  43)  whose  height  corresponds  to 
the  correct  position  of  the  crystal  as  given  by  Federow,  and 
is  equal  to  2c,  as  taken  by  Tutton). 

V  X  t                      w 

K,SO4                 64.92  4-464  4.491  4.997 

Rh,S04               73-36  4*634  4-664  5.237 

Cs.2SO4                84-64  4-846  4-885  5.519 

K2SeO4  71-71  4-636  4-662  5-118 

Rb2Se04  79-95  4-785  4-826  5.346 

Cs,Se04  91-16  4-987  5.03$  5-697 

As  is  seen,  in  both  series  the  increase  in  all  the  topic 
parameters  progresses  with  the  increase  in  the  atomic 
weights.  Further,  the  sulphate  of  any  one  of  the  three 
metals  stands  in  the  same  relation  to  the  corresponding 
selenate,  only  here  the  replacement  affects  the  acid-forming 
element  and  not  the  metal.  In  order  to  show  clearly 
that  a  similar  increase  in  the  dimensions  of  the  space  unit 
takes  place  on  the  replacement  of  one  of  these  elements  by 
one  of  higher  atomic  weight,  the  following  table  is  given 
containing,  in  addition  to  the  above,  the  data  for  potassium 
chromate  (which  also  shows  the  same  crystal  character) 
as  calculated  by  Gossner  from  Mitscherlich's  measurements 
and  his  own  density  determination. 

V                      x  t  w 

K2SO4                 64-92  4-464  4-491  4-997 

K2CrO4                70-39  4-600  4-647  5088 

KoSeO4                71-71  4-636  4-662  5-118 

As  already  stated,  those  compounds  which,  in  conse- 
quence of  the  similarity  in  the  morphotropic  effect  of  related 
elements,  show  a  very  close  agreement  in  their  crystal 
structure,  are  called  isomorphous  substances,  and  the 
elements  concerned  are  said  to  "  replace  one  another  iso- 


70  CHEMICAL  CRYSTALLOGRAPHY 

morphously."  For  example,  the  isomorphous  replacement 
of  chlorine  by  bromine  depends,  as  was  shown  on  page  67, 
on  the  nature  of  the  change  which  the  two  elements  produce 
in  the  crystal  structure  of  a  compound  when  each  is  intro- 
duced into  that  compound.  Since,  however,  this  change 
depends  also  on  the  nature  of  the  compound  in  which  the 
substitution  takes  place,  it  follows  that  the  variation  in 
the  effect  of  the  two  substitutions  (*>.,  the  extent  of 
the  differences  which  are  exhibited  by  the  two  resulting 
substances)  will  change  with  the  type  of  compound,  and  in 
general  will  be  smaller,  the  slighter  the  morphotropic  effects 
of  the  elements  themselves  in  that  particular  case. 

The  higher  the  degree  of  coincidence  in  the  crystal 
structures  of  two  isomorphous  substances,  the  greater  the 
coincidence  to  be  expected  with  regard  to  the  polymorphism 
which  they  exhibit.  Two  substances  which  are  capable 
each  of  existing  in  two  different  modifications,  these  corre- 
sponding in  pairs  and  standing  in  isomorphous  relationship, 
are  said  to  be  isodimorphous.  The  limiting  temperatures 
of  stability  for  the  two  modifications  are  always  different. 
For  example,  it  is  found  that  on  passing  from  a  chlorine  to 
a  bromine  derivative,  and,  still  more,  from  the  latter  to  an 
iodine  derivative,  the  melting  point  is  as  a  general  rule 
higher,  and  there  is  also  a  corresponding  displacement  of 
the  temperature  limits  of  stability  for  the  different  states. 
Therefore  it  often  happens  that  the  iodine  compound  (and 
not  infrequently  even  the  bromine  compound)  crystallises 
at  ordinary  temperatures  in  a  modification  which  is  different 
from  that  of  the  chlorine  compound ;  and  that  the  modifi- 
cation corresponding  to  the  latter  is  produced  only  at  higher 
temperatures.  In  all  series  of  inorganic  and  organic  sub- 
stances there  are  examples  of  this,  sufficient  to  justify  the 
assumption  that  chlorine,  bromine,  and  iodine  always 
replace  one  another  isomorphously,  and  that,  in  all  cases  in 
which  similar  compounds  of  these  elements  are  not  isomor- 
phous, this  difference  is  due  to  polymorphism.  If,  on  the 
other  hand,  we  compare  with  these  elements  the  first 


ISOMORPHISM  71 

member  of  the  halogen  group,  namely  fluorine,  we  find  that 
its  simpler  compounds  differ  greatly  from  those  of  chlorine, 
bromine,  and  iodine,  even  in  their  volume  relationships, 
and  as  a  rule  present  other  differences  in  crystal  structure. 
It  is  only  when  the  molecule  of  the  substance  in  which  the 
halogen  substitutions  are  affected  is  very  great,  and  the 
change  brought  about  by  the  substitution  is  consequently 
very  slight,  that  there  follows,  as  a  natural  consequence,  so 
close  an  agreement  between  the  fluorine  compound  and  the 
others  that  the  former  displays  the  properties  of  a  substance 
isomorphous  with  the  latter.  Fluorine,  therefore,  as 
regards  isomorphous  replacement,  shows  itself  to  be  less 
closely  related  to  chlorine  than  this  is  to  bromine  ;  and,  as 
is  well  known,  such  is  also  the  case  with  regard  to  its 
chemical  character.  In  all  groups  of  the  periodic  system 
of  the  elements,  this  applies  generally  to  the  relations 
between  the  first  member  and  the  next  one,  as  will  appear 
from  the  following  short  survey,  in  which  are  collected  the 
principal  facts  hitherto  observed  regarding  the  replaceability 
of  the  individual  elements,  these  being  arranged  in  groups  of 
like  valency.  Regarding  the  case  of  hydrogen,  which  is 
omitted  from  the  review,  it  has  already  been  shown  that  its 
replacement  by  a  univalent  metal  produces  a  change  which 
is  less  and  less  marked  the  larger  the  molecule  of  the  acid 
in  which  the  replacement  takes  place.  Hence  it  is  evident 
that  in  acids  of  an  extraordinarily  complex  nature  (as,  for 
example,  silicotungstic  acid,  H4SiW12O40,24H2O),  the  re- 
placement of  hydrogen  by  a  univalent  metal  may  exercise 
so  slight  an  influence  that  the  salt  and  the  acid  behave  like 
isomorphous  substances ;  likewise  in  many  complex  natural 
silicates,  isomorphous  replacement  of  the  alkali  metals  and 
hydrogen  must  be  assumed. 

I.  Group  of  the  alkali  metals  and  of  the  univalent  heavy  metals. — 
Lithium  chloride,  LiCl,  and  sodium  chloride,  NaCl,  both  crystallise 
cubic,  but  have  such  widely  different  equivalent  volumes  that  they 
cannot  be  considered  as  isomorphous.  The  periodates  of  these 
metals,  LiIO4  and  NaIO4,  possess  similar  tetragonal  forms, 


7:3  CHEMICAL  CRYSTALLOGRAPHY 

but  the  sulphates,  Li.jSO4  and  Na.2SO4,  exhibit  no  sort  of  agree- 
ment. Only  in  the  case  of  somewhat  more  complicated  com- 
pounds does  isomorphous  replacement  really  begin  ;  thus,  the 
following  salts  are  isomorphous  :  the  dithionates,  L5oS.,O6,2H2O 
and  Na2S2O6,2HoO  ;  the  manganophosphates,  LiMnPO4  and 
NaMnPQ,  ;  the  double  tartrates  with  thallium,  LiTlC4H4O6,2HoO 
and  NaTlC4H4O6,2H2O ;  and  others.  As  is  well  known, 
lithium,  sodium,  and  potassium  differ  from  one  another  in  that  the 
salts  of  the  first  two  often  crystallise  with  water  of  crystallisation, 
those  of  potassium,  on  the  other  hand,  without  it,  so  that  they  are 
not  comparable  with  the  former.  When,  however,  all  three 
metals  form  salts  which  are  anhydrous,  or  possess  the  same 
quantity  of  water  of  crystallisation,  it  is  found  that  the  metals  do 
not  replace  one  another  isomorphously  in  all  of  the  simpler 
compounds,  such  as  the  chlorides,  bromides,  iodides,  and  azides, 
the  chlorates,  bromates,  iodates,  and  all  the  simple  carbonates, 
sulphates,  and  chromates  ;  even  in  the  case  of  some  of  the  less 
simple  compounds,  such  as  the  double  magnesium  sulphates, 
Na2Mg(SO4)2,4H2O,  and  K2Mg(SO4).,,4HoO,  and  the  chloraurates, 
NaAuCl4,2H2O  and  KAuCl4,2HoO,  true  isomorphism  is  absent. 
The  following,  on  the  other  hand,  exhibit  agreement  in  crystallo- 
graphic  character:  the  double  carbonates,  Na«K1(COs)Al2H8O 
and  Na,K(CO.,)2,i2H2O  ;  the  alums,  NaAl(s64)"o,i2H2O  and 
KA1(SO4)2I2H2O  ;  the  monohydrogen  phosphates,  Na2HPO4,7H2O 
and  NaKHPO4,7H2O  ;  also  the  phthalates,  Na2C8H4O4  and 
K-jCHH4O4,  and  the  0-toluenesulphonates,  NaSO.,C7H6  and 
KSO3C7H6;  whilst  the  w-dinitrobenzoates,  NaC^O^NOo).,  and 
KC7H:»O.,(NOo).,,  are  not  isomorphous.  In  complicated  natural 
silicates  also,  lithium  and  sodium  exhibit  distinct  differences  from 
potassium  (in  the  tourmalines,  for  example),  whilst  in  others  (such 
as  vesuvianite),  potassium,  sodium,  lithium,  and  hydrogen  may 
vicariously  represent  one  another.  The  difference  of  character 
between  sodium  and  potassium  is  further  exhibited  by  the  fact  that 
in  some  salts  they  occur  side  by  side  as  constituents  in  definite 
atomic  proportions,  as  in  glaserite,  NaK:,(SO4)2,  and  the  double 
tartrate  (Rochelle  salt),  NaKC4H4O6,H2O  ;  the  same  is  seen  with 
lithium  and  potassium  (in  the  double  sulphate,  LiKSO4 ;  double 
racemate,  LiKC4H4O6,H2O  ;  and  others). 

On  the  other  hand,  the  isomorphous  replacement  of  potassium, 
rubidium,  and  caesium  is  quite  general,  in  simple  compounds  as 
in  complex.  Thus,  their  halides,  nitrates,  iodates,  sulphates  (see 
page  69),  and  selenates— both  single  and  double  salts — are  com- 


ISOMORPHISM  73 

pletely  isomorphous,  as  are  also  the  respective  salts  of  the  most 
widely  varying  organic  acids  (see,  for  example,  page  66).  Only  in 
a  few  cases  do  apparent  exceptions  arise,  owing  to  the  salts  being 
polymorphous  ;  thus,  one  particular  modification  of,  say,  the 
potassium  salt,  may  be  known,  whilst  in  the  case  of  the  rubidium 
or  caesium  salt  only  some  other  modification  may  be  known, 
owing  to  the  different  situation  of  the  transition  temperature. 
Ammonium  behaves  chemically  exactly  like  an  alkali  metal,  and 
accordingly  the  ammonium  salts  are  generally  isomorphous  with 
the  analogous  potassium,  rubidium,  and  caesium  salts  ;  in  the  case 
of  the  sulphates,  it  was  shown  by  Tutton  that  the  crystallographic 
and  physical  constants  of  the  ammonium  compounds  lie  between 
those  of  the  rubidium  and  caesium  compounds,  but  very  near  to 
the  former,  and  in  other  isomorphous  groups  similar  conditions 
seem  to  apply.  On  the  other  hand,  the  limiting  temperatures  of 
stability  of  a  particular  polymorphous  modification  are,  in  the  case 
of  the  ammonium  salt,  often  strikingly  different  from  those  for  the 
potassium  salt,  and  on  this  ground  it  very  often  happens  that  in 
the  case  of  analogous  compounds  the  potassium  salt  is  observed 
in  a  different  crystalline  form  from  the  ammonium  salt.  How,  in 
such  cases  (e.g.,  the  acid  sulphates,  the  chlorides,  and  the 
thiocyanates),  the  proof  of  the  isodimorphism  of  the  salt  group  is 
furnished,  will  be  indicated  in  one  of  the  following  sections 
("Isomorphous  Mixtures").  For  the  isomorphism  of  the  salts  of 
univalent  thallium  with  the  corresponding  potassium  salts,  there 
are  numerous  examples  also,  such  as  :  the  azides,  T1N3  and  KN3  ; 
the  nitrates,  T1NO3  and  KNO3  ;  the  periodates,  T1IO4  and  KIO4 ; 
various  sulphates,  chromates,  selenates,  and  particularly  the 
corresponding  double  sulphates  ;  finally,  the  oxalates,  racemates, 
picrates,  and  others. 

The  univalent  metals,  copper,  silver,  and  gold,  in  the  form  ot 
the  crystallised  elements,  constitute  an  undoubtedly  isomorphous 
group,  and  the  first  two  also  replace  each  other  isomorphously  in 
a  number  of  native  sulphur  compounds,  as  also  in  the  following 
complicated  salts  :  the  triple  thiocyanates,  Cs3SrCu.2(SCN)7  and 
Cs3SrAg2(SCN)7;  and  the  compounds  NH4Cl,CuCl,4(NH4)2S2O3 
and  NH4Cl3AgCl,4(NH4)2S2O3.  The  non-similarity  of  other  com- 
pounds of  these  metals  (for  example,  the  relatively  simple  double 
cyanides  KCu(CN)2  and  KAg(CN)2)  may  possibly  be  due  to 
polymorphism.  Sodium,  as  regards  isomorphism,  exhibits  very 
close  relations  with  silver.  This  is  particularly  noticeable  with 
the  chlorides,  nitrates,  iodates,  sulphates,  and  dithionates,  but 


74  CHEMICAL  CRYSTALLOGRAPHY 

the  question  of  the  isomorphous  replacement  of  these  two  metals 
requires  further  investigation. 

II.  Group  of  the  bivalent  metals. — Beryllium,  in  agreement 
with  magnesium  and  zinc,  crystallises  hexagonal,  and  further,  the 
form  of  beryllium  oxide  exhibits  certain  analogies  with  that  of 
zinc  oxide  ;  nevertheless  an  isomorphous  replacement  of  beryllium 
by  other  bivalent  metals  in  analogous  salts  has  been  found  only  in 
few  cases.  Beryllium  aluminate  and  chromite,  Be(AlOo)2  and 
Be(CrO2).>,  crystallise  differently  from  the  magnesium  salts, 
Mg(Al<52).2  and  Mg(CrO2),j,  whilst  the  double  phosphates, 
NaBePO4  and  NaMnPO4,  exhibit  very  similar  forms.  In  some 
other  phosphates,  as,  for  example,  the  mineral  groups  of  wagnerite, 
MgMgFPO4,  and  herderite,  CaBeFPO4,  more  intimate  relations 
between  beryllium  and  the  other  bivalent  metals  may  be  recognised. 
Among  the  silicates,  only  phenacite,  BeoSiO4,  and  willemite, 
Zn2SiO4,  are  comparable,  because  the  salts  of  other  metals, 
corresponding  in  composition  to  the  remaining  beryllium  silicates 
(and  therefore  potentially  isomorphous  with  them)  are  unknown. 
Further,  there  exist  no  normal  beryllium  salts  of  the  fatty  acids. 

Very  many  groups  of  analogously  constituted  salts  of  the 
bivalent  metals  magnesium,  manganese,  iron,  nickel,  cobalt,  zinc, 
and  cadmium,  derived  from  the  most  various  acids,  organic  as 
well  as  inorganic,  have  been  crystallographically  determined  ; 
with  these  it  is  regularly  found  that  there  is  a  very  complete 
isomorphism  of  all  the  members  of  any  such  group.  The  same 
applies  to  the  hydroxides,  and  also,  to  a  certain  extent,  to  the 
elements  themselves.  In  the  few  cases  in  which  apparent  ex- 
ceptions to  this  rule  are  found,  as  with  magnesium  sulphate  and 
ferrous  sulphate,  it  can  be  shown  beyond  doubt  that  the  respective 
salts  are  isodimorphous  (see  under  "Isomorphous  Mixtures," 
page  91).  Bivalent  copper  in  the  simpler  compounds  appears 
to  stand  apart  from  the  above-mentioned  metals,  but  in  more 
complex  salts  it  takes  its  place  beside  them  ;  thus  the  fluosilicate, 
CuSiF6J6H.,O,  is  isomorphous  with  the  corresponding  salts  of 
magnesium,  manganese,  iron,  nickel,  cobalt  and  zinc  ;  also  the 
fluozirconate,  Cu^Zrl  •'..  12!  I ,(),  with  that  of  zinc;  the  sulphate, 
CuSO4,5H2O,  and  double  sulphate,  K2Cu(SO4).2,6H2O,  with  those 
of  magnesium,  manganese,  iron,  cobalt,  zinc,  and  cadmium  ;  but 
whilst  the  double  sulphates  of  the  other  metals  agree  very  closely 
among  themselves  as  regards  their  angles,  the  copper  salt  in  this 
respect  stands  dist'mrtly  apart.  FurilM-r  examples  arc  supplied 


ISOMORPHISM  75 

by:  the  basic  arsenate,  Cu2OHAsO4,  isomorphous  with  the 
zinc  salt,  ZnoOHAsO4 ;  the  acid  arsenate,  CuHAsO4H.2O,  with 
the  zinc  salt,  ZnHAsO^HoO  ;  sodium  cupric  uranyl  acetate, 
NaCu(UOo)3(C2H3Oo)9,9H.2O,  with  the  corresponding  magnesium 
(see  page  5),  manganous,  ferrous,  nickel,  cobaltous,  and  zinc 
salts  ;  further,  also,  the  formates,  malates,  benzenesulphonates,  etc., 
of  these  same  metals.  Finally,  bivalent  vanadium  appears  in 
certain  compounds  isomorphously  replacing  the  above  metals  ; 
namely,  in  the  heptahydrated  sulphates  and  in  the  double  sulphates 
of  the  K2Mg(SO4)2,6H2O  type. 

A  further  group  of  elements  which  regularly  replace  one  another 
isomorphously  is  that  of  the  metals  calcium,  strontium,  barium, 
and  lead.  The  oxides,  the  hydrated  chlorides,  and  the  azides  of 
calcium,  strontium,  and  barium  crystallise  respectively  alike  ;  in 
addition  to  these,  the  lead  salt  is  also  isomorphous  in  the  case  of 
the  nitrates,  bromates,  carbonates,  sulphates,  etc.,  and  there  are 
isomorphous  salts  of  these  metals  known,  derived  from  many 
organic  acids.  In  many  cases  the  calcium  salt  appears  different 
from  the  others  (the  propionate,  for  example,  which  even  forms 
double  compounds  with  the  propionates  of  strontium,  barium,  and 
lead),  also  the  tartrate  and  malate.  Even  when  the  calcium  salt  is 
isomorphous  with  the  others,  its  angles  as  a  rule  exhibit  greater 
differences  from  those  of  the  isomorphous  salts  than  these  do 
among  themselves.  The  somewhat  exceptional  position  of  the  first 
member  of  this  series  of  metals  further  appears  from  the  fact  that 
the  calcium  salt  can  also  functionate  as  a  replacer  of  the  previously 
mentioned  series  of  metals  which  begins  with  magnesium.  The 
salts  of  these  two  series  of  metals  are  in  general  not  isomorphous, 
and  in  many  cases  they  crystallise  with  unequal  amounts  of  water 
of  crystallisation,  which  of  itself  excludes  all  comparison.  In  some 
cases,  however,  the  isomorphous  replacement  of  calcium  and 
magnesium  by  each  other  cannot  be  doubted,  as  in  the  carbonates 
(calcite  and  magnesite) ;  but  these  form  in  addition  a  double 
compound  (dolomite),  containing  equal  atomic  proportions  of 
calcium  and  magnesium  ;  this,  though  it  possesses  similar  form, 
is  of  lower  symmetry.  A  similar  state  of  affairs  exists  with 
the  silicates,  as  shown  by  the  minerals  diopside,  CaMg(SiO3).2, 
and  forsterite,  CaMgSiO4 ;  in  these  the  magnesium  can  be 
replaced  by  other  metals  of  the  same  series,  such  as  manganese, 
iron,  etc.  Still  rarer  than  these  are  the  cases  in  which  strontium 
and  barium  can  replace  a  metal  of  the  magnesium  series  ;  above 
700°  strontium  carbonate  is  isomorphous  with  calcium  car- 


76  CHEMICAL  CRYSTALLOGRAPHY 

bonate,  and  therefore  with  magnesite ;  and  barium  tungstate, 
2Ba\V4O13,i9HoO,  is  isomorphous  with  the  corresponding  cobalt  salt, 
2CoW4O1;tti9H2O.  On  the  other  hand,  the  difference  between  the 
two  series  appears  very  distinctly  in  the  non-existence  of  a  cubic 
calcium  spinel,  whilst  for  all  bivalent  metals  of  the  magnesium 
series  the  spinels  supply  an  exceptionally  good  example  of  their 
isomorphous  replaceability  ;  further  examples  are  :  the  arsenates 
of  the  MgHAsO4,HoO  type  ;  the  formates,  which  differ  from  those 
of  the  calcium  series  even  in  the  amount  of  water  of  crystallisation, 
and  which  also  form  double  salts  with  lead  formate  ;  the  acetates, 
malonates,  and  other  salts. 

In  the  periodic  system  of  the  elements  the  metals  of  the 
platinum  group  stand  in  close  relation  to  those  of  the  iron  group, 
and,  in  accordance  therewith,  the  members  of  both  are  capable  of 
isomorphously  replacing  one  another,  as  is  shown  by  the  complete 
agreement  of  sperrylite,  PtAs.,,  and  laurite,  RuSo,  with  the  cor- 
responding iron-group  compounds  which  constitute  the  pyrites 
group  of  minerals,  and  also  by  the  perfect  isomorphism  of  potas- 
sium palladiocyanide,  KoPd(CN)4,HoO,  with  the  nickelocyanide, 
K2Ni(CN)4,H2O.  Tin,  through  the  analogy  of  certain  compounds, 
associates  itself  with  the  platinum  metals,  so  that  isomorphous 
relationships  with  stannous  compounds  were  to  be  expected,  as 
between  these  and  the  compounds  of  bivalent  lead,  mercury,  and 
copper.  Apart  from  similarities  in  the  crystallographical  relation- 
ships of  stannous  chloride,  SnCL,  and  lead  chloride,  PbCL  ;  of 
mercuric  oxide,  HgO,  and  lead  oxide,  PbO  ;  of  cupric  sulphide, 
CuS,  and  mercuric  sulphide,  HgS,  it  is  found  that  the  potassium 
'double  chlorides,  KoSnCl4  and  K2HgCl4,  as  also  the  ammonium 
salts,  (NH4),SnCl4,2H-,O  and  (NH4),HgCl4,2H,O,  exhibit  such 
closely  agreeing  forms  that  they  must  be  assumed  to  be  really 
isomorphous.  Further,  copper  and  mercury  replace  each  other 
in  the  isomorphous  compounds  of  types  (N(CH:1)4)2RC14  and 
(N(C,Hr,)4).,RCl4,  and  in  the  compounds  of  quinoline  hydrochloride 
with  cupric  and  mercuric  chlorides,  described  by  Borsbach. 

III.  Group  of  the  trivalent  elements. — The  relations  of  the  first 
member  of  this  group  (boron)  to  those  elements  which  follow  it, 
are  limited  to  the  similarity  which  the  monoclinic  crystals  of 
hydrargyllite,  A1(OH)3,  exhibit  with  the  triclinic  crystals  of 
sassoline,  B(OH)3,  and  to  the  analogy  of  the  role  played  by  boron 
and  aluminium  in  some  complicated  silicates.  On  the  other  hand, 
aluminium  is  quite  generally  R-jjl.-ut-d  by  trivalent  chromium, 


ISOMORPHISM  77 

manganese,  and  iron,  and,  not  infrequently,  also  by  titanium. 
Examples  are  supplied  by  the  oxides,  ALO  ,  Ti._,O:j,  Cr2Oa,  Fe.2O:J ; 
the  hydroxides,  A1O.OH,  MnO.OH,  FeO.OH  ;  the  various 
aluminium  and  ferric  sulphates,  silicates  (here  titanium  also,  e.g.^ 
in  the  garnet  group),  etc.  ;  also  the  salts  in  which  the  metallic 
oxides  represent  the  acidic  constituent,  as  in  the  spinels,  Mg(AlO.2)._>, 
Mg(CrO2)2,  Mg(MnO2)2,  Mg(FeO.2)2.  The  isomorphous  replace- 
ment of  the  most  widely  varying  trivalent  metals  has  been  shown 
with  great  completeness  in  the  group  of  the  alums,  which  are,  it 
is  true,  fairly  complex  compounds  ;  in  these  the  aluminium  of 
common  alum,  KA1(SO4).2,I2H2O,  maybe  replaced  by  any  of  the 
following : — vanadium,  chromium,  manganese,  iron,  cobalt, 
gallium,  rhodium,  indium,  thallium  (?),  titanium.  There  is 
probably  also  isomorphism  between  compounds  of  trivalent 
indium  and  thallium  in  the  case  of  certain  double  chlorides. 

The  trivalent  metals  of  the  so-called  rare  earths  replace  one 
another  isomorphously  in  the  hydrated  sulphates,  which  have  been 
very  completely  investigated,  but  isomorphism  between  the  salts  of 
these  metals  and  the  corresponding  salts  of  iron  or  aluminium,  has 
been  proved  only  in  the  case  of  some  complicated  silicates,  such  as 
orthite.  Isomorphism  is  also  assumed  to  exist  between  certain 
complex  double  nitrates  of  the  rare-earth  metals  and  those  of 
bismuth,  but  this  has  not  yet  been  sufficiently  proved  by  a 
comprehensive  crystailographic  investigation. 

Amongst  the  platinum  metals,  two  (rhodium  and  iridium) 
appear  as  trivalent  in  a  series  of  compounds,  and  here  again 
cases  of  isomorphism  occur,  for  example, — the  complex  cyanides, 
K3Ir(CN)6  and  K,Rh(CN)6,  with  K.C^CN)^  K3Mn(CN)c, 
KoCo(CN)6,  and  K,Fe(CN)6 ;  the  ammonia  addition  compounds, 
Ir(NO:!)3,6NH3  with  Co(NO,)3,6NH,,  and  Cl.2Rh2(NH,),0Cl4 
with  CLCo2(NH3)10Cl4  (chloropurpureo-cobaltichloride). 

IV.  Group  of  the  quadrivalent  elements. — The  profound 
differences  which  the  first  and  second  members  of  this  group 
(carbon  and  silicon)  exhibit  from  the  chemical  point  of  view, 
are  reflected  in  the  fact  that,  except  for  the  agreement  between 
the  cubic  crystalline  forms  of  the  two  iodides,  CI4  and  SiI4,  there 
is  no  isomorphism  between  analogously  constituted  compounds 
of  the  two  elements — between  the  carbonates  and  the  silicates, 
for  example — and  also  in  the  fact  that  the  two  elements  unite  to 
form  a  very  stable  compound,  CSi  (carborundum),  whose  crystal- 
line form  exhibits  no  relation  to  that  of  either  of  its  elements. 


7-  CHEMICAL  CRYSTALLOGRAPHY 

On  the  other  hand,  silicon  can  be  isomorphously  replaced  by 
titanium  and  by  tin.  Although  the  form  of  silica  corresponding 
to  the  isomorphous  dioxides  rutile,  TiOo,  and  cassiterite,  SnO._>, 
is  unknown  (as  is  also  that  of  zirconia,  ZrO2) ;  and,  further,  the 
agreement  between  the  crystalline  forms  of  the  iodides  SiI4,  TiI4, 
SnI4,  and  between  the  compounds  of  phosphoric  anhydride  with 
the  dioxides  of  silicon,  titanium,  zirconium,  and  tin,  is  in  each  case 
discounted  to  a  certain  extent  by  reason  of  these  substances  all 
belonging  to  the  cubic  system,  the  isomorphous  replacement  of 
these  elements  appears  indubitably  in  a  series  of  fluo-salts,  such  as 
those  of  the  types  SrSiF6,2H2O,  MgSiF6,6H2O,  etc.  In  the 
isomorphous  group  of  chloro-salts  corresponding  to  the  last- 
mentioned  type  of  fluo-salt,  platinum  also  appears  replacing  tin 
isomorphously ;  the  anhydrous  salts,  K2SnCl6  and  K2PtCl6  (as 
also  KoPdCl6,  etc.),  are  also  isomorphous  ;  so  also  are  the 
chloroplatinates  and  chlorostannates  of  a  great  variety  of  alkyl- 
ammonium  radicals.  Further,  the  chloro-salts  K2TeCl6,  CsoPbCl,., 
and  Cs2SbCl6  crystallise  in  the  octahedral  form  which  is  char- 
acteristic of  the  similarly-constituted  salts  K2SnCl6  and  Cs._,PtClti. 
The  relation  here  observed  between  quadrivalent  lead  and  tin 
occurs  again  in  the  isomorphism  of  the  acid  fluo-salts  K;jHSnF8 
and  K;,HPbF8.  Finally,  quadrivalent  cerium  appears  to  be 
isomorphous  with  thorium  in  the  nitrates  MgRIV(NO:{)r,,8H2O,  and 
the  latter  element  with  uranium  in  the  sulphates  Th(SO4)._>,9H.,O 
and  U(SO4).3,9H2O. 

V.  The  nitrogen  group  (trivalent  and  quinquivalent  elements). — 
As  is  to  be  expected  from  the  chemical  characters,  isomorphous 
relationships  are  in  general  not  observed  between  nitrogen  and  the 
succeeding  elements  of  this  group.  Thus,  even  the  tetra-alkyl- 
phosphonium  bromides  and  iodides  crystallise  differently  from  the 
corresponding  ammonium  derivatives  ;  and,  similarly,  triphenyl- 
amine,  N(C6H5);!,  notwithstanding  the  size  of  its  molecule,  differs 
from  the  corresponding  substances  P(C6H5),,  As(CcH5)3,  Sb(C6H5), 
and  Bi(C6H5)3.  On  the  other  hand,  the  chloroplatinates  of 
tetraethylammonium,  tetraethylphosphonium,  and  tetraethyl- 
arsonium  (all  cubic,  however)  may  possibly  be  considered  as 
isomorphous. 

With  phosphorus  there  begins  a  series  of  elements  which 
replace  one  another  isomorphously  in  the  most  diverse  classes  of 
compounds,  and  which  even  can  assume  similar  crystal  forms 
in  the  free  state  ;  these  are  phosphorus,  arsenic,  antimony,  and 


ISOMORPHISM  79 

bismuth.  Amongst  those  compounds  in  which  these  elements  have 
a  trivalent  character  there  is  regularly  isomorphous  replacement 
— in  the  oxides,  sulphides,  iodides,  and  especially  in  numerous 
natural  thio-salts  (the  thiarsenites,  thiantimonites,  and  thio- 
bismuthites).  As  quinquivalent  elements,  phosphorus,  vanadium, 
and  arsenic  replace  one  another  in  the  apatite — Ca5Cl(PO4);{ — 
group,  and  in  numerous  isomorphous  groups  of  hydrated  phos- 
phates and  arsenates  (the  corresponding  vanadates  have  been 
less  fully  investigated  crystallographically) ;  the  compounds 
P(C2H5)3(C2H4Br)Br  and  As(C2H5)3(C2H4Br)Br,  which  crystallise 
cubic,  can  also  be  looked  upon  as  isomorphous. 

Whilst  niobium  and  tantalum  replace  one  another  isomorphously 
in  all  known  cases  (fluo-compounds,  tantalates  and  niobates)  the 
question  of  the  isomorphism  of  the  oxides  Nb.2O5  and  Ta2O5  with 
V._>O5  requires  further  investigation. 

VI.  Oxygen  group  (bivalent,  quadrivalent,  and  sexivalent 
elements). — A  true  isomorphous  replacement  of  oxygen  by  the 
succeeding  members  of  the  group  does  not  exist,  and  even  very 
complicated  sulphur  compounds  are  not  isomorphous  with  the 
corresponding  oxygen  compounds  ;  thus,  the  thiosulphates 
crystallise  differently  from  the  sulphates,  and  not  only  carbamide 
(urea)  and  thiocarbamide,  but  also  their  phenyl  derivatives — even 
diphenylcarbamide  and  thiocarbanilide,  notwithstanding  the  size 
of  their  molecules — are  different.  On  the  other  hand,  there  is 
unmistakably  a  certain  analogy  in  the  cubic  structure  of  certain 
exceedingly  simple  compounds  of  the  two  elements,  as  between 
cuprous  oxide  and  sulphide,  magnesium  oxide  and  sulphide,  zinc 
oxide  and  sulphide  (in  this  case  there  is  also  agreement  in  the 
symmetry  for  a  second — a  hexagonal — modification) ;  also  between 
the  oxides  and  sulphides  of  calcium,  strontium,  and  barium  ;  and, 
finally,  between  the  spinels  and  certain  analogous  thio-salts 
(linneite,  Ni3S4).  The  agreement  between  certain  metallic  tellur- 
ides,  which  crystallise  cubic,  and  the  corresponding  sulphides  and 
selenides,  must,  in  the  same  way,  be  looked  upon  as  constituting 
no  true  isomorphism  ;  the  other  compounds  of  tellurium  do  not 
agree  crystallographically  with  the  compounds  of  sulphur  and  of 
selenium. 

In  this  group  the  most  important  series,  as  regards  isomorphous 
replacement,  are  formed  by  the  elements  sulphur,  chromium,  and 
selenium,  when  these  have  a  sexivalent  character.  The  rhombic 
potassium  salts,  K._>SO,,  K._,CrO4,  and  K2SeO4,  have  been  mentioned 


80  CHEMICAL  CRYSTALLOGRAPHY 

already  (page  69),  and  with  these  are  also  to  be  ranged  KoMnO4 
and  K2FeO4,  possibly  also  K,MoO4  and  K2WO4 ;  these  two  have 
not  yet  been  prepared  in  suitable  crystals  (the  thio-salts  cor- 
responding to  them  exhibit  a  certain  analogy  of  crystalline  form 
with  the  preceding  salts).  Ammonium  chromate  and  molybdate 
are  isomorphous  with  the  monoclinic  form  of  the  selenate,  and 
isomorphism  has  also  been  established  between  ammonium 
magnesium  sulphate,  (NH4)2Mg(SO4)o,6H.2O,  and  the  correspond- 
ing molybdate,  (NH4).,Mg(MoO4).,,6H2O,  and  also  between 
the  three  magnesium  salts,  MgSO4,5HoO,  MgCrO4,5HoO,  and 
MgMoO4,5H2O.  In  addition  to  the  quite  general  isomorphism 
between  analogous  sulphates  and  selenates,  isomorphism  is  also 
observed  not  only  with  the  chromates  and  the  molybdates,  but  also 
with  the  tungstates,  in  salts  of  the  type  Na3Li(SO4)o,6H2O  and 
those  of  the  type  of  Glauber's  salt,  Na.2SO4,ioH2O.  Isomorphism 
is  also  regularly  observed  in  analogously  constituted  molybdenum 
and  tungsten  compounds,  such  as  the  normal  molybdates 
and  tungstates  of  calcium,  strontium,  barium,  and  lead  ;  the 
compounds  (NH4)2MoOoF4  and  (NH4)>WO2F4,  and  other  similar 
salts. 

VII.  The  fluorine  group. — It  has  been  already  mentioned  on 
page  71,  that,  as  regards  isomorphism,  fluorine  appears  less  closely 
related  to  the  other  halogens  than  these  are  among  themselves. 
As  a  matter  of  fact,  the  fluorides  KF  and  NH4F  crystallise  differ- 
ently from  the  chlorides  KC1  and  NH4C1,  and  SnF2  differently  from 
SnCl2 ;  and  the  agreement  in  the  crystalline  forms  of  the  sodium 
salts,  NaF  and  NaCl,  is  not  decisive,  because  here  we  have  to  deal 
with  cubic  substances.  An  actual  isomorphism  between  cor- 
responding compounds  of  fluorine  and  chlorine  becomes  recog- 
nisable only  when  the  compounds  are  of  a  complex  nature, 
such  as  the  magnesium  halogeno-stannates,  MgSnF6,6H2O  and 
MgSnCl6,6H3O  ;  the  apatites,  Ca5F(PO4);t  and  Ca5Cl(PO4);1 ;  the 
fluo-  and  chloro-naphthalenesulphonic  chlorides,  and  the  ethyl 
esters  derived  from  them. 

On  the  other  hand,  as  mentioned  on  page  70,  chlorine,  bromine, 
and  iodine  replace  one  another  isomorphously  in  all  compounds  ; 
the  exceptions  to  this  generalisation  are  only  apparent,  and  are  due 
to  the  fact  that  the  compound  containing  iodine  (or  bromine  and 
iodine)  forms  the  corresponding  modification  only  at  a  higher 
temperature.  A  well-known  example  of  this  is  provided  by  the 
group  of  the  silver  halides,  AgCl,  AgBr,  and  Agl  :  the  first  and 


ISOMORPHISM  si 

second  crystallise  cubic ;  the  last  crystallises  at  ordinary 
temperatures  in  a  hexagonal  form,  its  cubic  modification,  isomor- 
phous  with  the  others,  being  stable  only  at  higher  temperatures. 
Ammonium  bromide  is  isomorphous  with  ammonium  chloride, 
but  ammonium  iodide  is  not ;  although  it  also  crystallises  cubic, 
the  modification  is  one  which  corresponds  to  that  of  the  three 
halides  of  potassium,  which  are  completely  isomorphous  ;  the  cor- 
responding modification  of  ammonium  chloride  is  produced  only 
at  higher  temperatures.  The  exceptional  character  of  the  iodine 
compound,  due  to  polymorphism,  appears  also  in  the  iodides  of  the 
bivalent  metals,  such  as  mercury,  and  those  of  the  trivalent  metals, 
such  as  antimony  ;  whilst  in  the  case  of  the  double  halides  all  three 
compounds,  as  a  rule,  belong  to  the  corresponding  modification  at 
the  ordinary  temperature  ;  the  same  is  the  case  with  still  more 
complex  compounds,  as  in  the  apatites,  where  the  fluorine,  chlorine, 
bromine,  and  iodine  compounds  are  completely  isomorphous.  On 
the  other  hand,  only  sodium  bromate,  NaBrO3,  agrees  with  the 
chlorate,  NaClO3— the  iodate,  NaIO3,  crystallising  differently.  The 
corresponding  potassium  salts  are  all  different  from  one  another, 
and  it  is  evident  that  in  this  group  very  complicated  polymerism 
obtains.  As  regards  a  chlorine  compound  and  the  corresponding 
bromine  compound,  however,  in  by  far  the  great  majority  of  cases 
the  limits  of  stability  for  other  possible  modifications  are  such  that 
at  ordinary  temperatures  the  two  substances  are  obtained  in  cor- 
responding states,  and  these  two  substances  are  then  completely 
isomorphous — as  a  rule  with  very  close  agreement  in  the  angles  ; 
somewhat  greater  angle  differences  manifest  themselves  only  in 
cases  where  the  equivalent  volumes  of  the  two  substances  are 
appreciably  different  from  each  other,  as  with  /-dichlorobenzene 
and  /-dibromobenzene. 

Although  there  are,  amongst  the  examples  collected  in 
the  preceding  paragraphs,  some  whose  isomorphous  re- 
lationships would  require  to  be  subjected  to  a  more  thorough 
investigation,  it  is  nevertheless  amply  evident,  from  the  well- 
established  facts,  that  the  atoms  of  two  closely  related 
elements  possessing  the  same  valency  are  capable  of  replac- 
ing each  other  without  the  crystal  structure  thereby  under- 
going any  extensive  change.  The  same  holds  also  for  the 
replacement  of  the  potassium  atom  by  the  ammonium 
radical,  NH4,  in  accordance  with  the  complete  chemical 

F 


82  CHEMICAL  CRYSTALLOGRAPHY 

analogy    between    ammonium    and    the    univalent    alkali 
metals. 

The  cyanogen  radical,  CN,  in  its  chemical  relations 
behaves  very  like  a  halogen,  and  it  is,  therefore,  natural  to 
expect  the  isomorphous  replaceability  of  cyanogen  and 
the  halogens.  If,  however,  the  existing  observations  are 
examined,  then  (apart  from  the  salts  of  the  alkali  metals, 
whose  mere  similarity  of  form  is  no  criterion,  since  they 
belong  to  the  cubic  system)  it  is  found  that  there  is  in 
general  no  similarity  of  crystallographic  character  ;  in  most 
cases,  also,  the  cyanogen  compounds  which  in  composition 
correspond  to  the  complex  halides,  either  do  not  exist,  or, 
if  they  do  (as  in  the  case  of  potassium  ferricyanide  and  the 
analogous  chloro-salts  and  fluo-salts),  the  question  of  their 
isomorphism  has  not  been  investigated. 

On  the  other  hand,  a  not  inconsiderable  number  of 
cases  have  been  established,  in  which  two  compounds, 
differing  from  one  another  by  the  replacement  of  an  atom 
by  an  atomic  group  of  similar  valency,  exhibit  such 
thorough  agreement  in  crystallographical  character  that 
they  have  been  designated  as  isomorphous  substances. 
Such  relationships  are  exhibited,  for  example,  by  certain 
minerals  containing  hydroxyl  and  fluorine  (wagnerite  group, 
topaz),  and  these  have  given  rise  to  the  assumption  of  an 
isomorphous  replacement  of  fluorine  and  hydroxyl.  (An 
attempt  by  Pels,  to  discover  isomorphism  between  chlorine 
derivatives  and  hydroxyl  derivatives  of  benzene,  was 
without  result,  probably  owing  to  the  fact  already 
mentioned,  that,  as  regards  isomorphism,  the  chlorine 
compounds  diverge  considerably  from  the  corresponding 
fluorides.)  Of  organic  fluorine  compounds  suitable  for 
comparison,  only  a  few  have  been  closely  investigated, 
but,  as  a  matter  of  fact,  one  case  described  by  Gossner  like- 
wise shows  such  close  relationships  between  the  respective 
substances,  as  to  justify  the  conclusion  that,  in  substances 
of  complex  composition,  an  isomorphous  replacement  of 
hydroxyl  and  fluorine  can  really  take  place.  In  the  same 


ISOMORPHISM  83 

way  it  is  possible  that  in  the  minerals  related  to  sodalite 
the  replacement  of  chlorine  by  other  salt  radicals  is  to  be 
explained  by  the  size  of  the  molecule.  On  the  other  hand, 
it  is  scarcely  possible  to  include,  under  the  heading  of 
isomorphism  in  the  stricter  sense,  the  striking  resemblances 
in  crystalline  form  which,  according  to  Hiortdahl's  observa- 
tions, the  salts  of  the  univalent  radicals  Sn(CH3)3,  Sn(C2H5)3, 
etc.,  exhibit  with  the  corresponding  salts  of  the  univalent 
metals  (as  do  also  the  analogous  salts  of  the  bivalent  radicals, 
SnR2,  with  those  of  bivalent  metals)  ;  these  relationships, 
however,  merit  further  investigation. 

The  researches  of  Marignac  have  resulted  in  the  recog- 
nition of  the  complete  analogy  in  crystalline  character  of 
the  members  of  several  different  series  of  salts,  where  the 
various  members  of  any  one  series  differ  among  themselves, 
as  regards  chemical  character,  in  having  the  bivalent  group 

IV  IV 

TiF2,  or  SnF2, 
replaced  by  the  groups  (likewise  bivalent) 

NbOF,  MoO2  and  WO2, 

which  must,  therefore,  be  looked  upon  as  replacing  one 
another  isomorphously.  In  the  following  table  several 
series  of  this  kind  are  expressed  by  formulae  which  are  so 
written  that  the  groups  above  mentioned  appear  separated 
from  the  other  constituents  : 

O  __  TT*         "G*    T*^    T  T 

bni<2  .  t<6K3.b. 
NbOF .  F6K3H 

TiF2.F4K2,  H20  ] 
NbOF .  F4K2,  H,O  - 
WO2 .  F4K2,  H20  J 

TiF2.F4Cu,  4H20 
NbOF .  F4Cu,  4H2O 
WO2.F4Cu,  4H2O 


84  CHEMICAL  CRYSTALLOGRAPHY 

SnF.,.F4Zn,  6H,0     1 

XbOF.F4Zn,  6H0O 

Mo02.F4Zn,  6H26    J 

Though  the  constitution  of  the  substances  here  dealt 
with  can  by  no  means  be  considered  as  clearly  established, 
there  is,  on  the  other  hand,  an  unmistakable  agreement  of 
crystal  form  in  the  case  of  organic  compounds  of  well- 
established  constitution,  which  likewise  differ  from  one 
another  by  the  mutual  replacement  of  radicals  of  like 
valency  but  dissimilar  constitution.  A  number  of  such 
cases  are  given  here. 

The  carboxyl  group,  —CO.  OH,  and  the  sulphonyl  group, 
— SO2 .  OH,  possess  a  similar  chemical  character.  As  Zirngiebl  has 
shown,1  there  is  a  great  similarity  in  the  crystallographical  relation- 
ships of  the  analogous  salts  of  phthalic  acid, 

/CO. OH 

C6H4( 

\CO .  OH 

and  of  0-sulphobenzoic  acid, 

/SO,.  OH 
C6H4( 

\CO.OH; 

notwithstanding  the  relatively  great  difference  between  the  equiva- 
lent volumes,  this  similarity  extends  even  to  the  values  of  the  topic 
parameters.  There  is,  further,  a  similar  relation  between  benzoic 
acid,  C6H5.CO.OH,  and  benzene  sulphonic  acid,  C6H,,.SO.,OH  ; 
and,  finally,  between  sulphoacetic  acid, 

/CO.  OH 
CH,( 

\SO.,.OH 


and  methionic  acid, 


/SO.,.  Oil 
(  i! 

\SO.2.OH 


The  alkali  metal  salts  of  imido-sulphonic  acid  are  crystallo- 
graphirally  very  closely  similar  to  those  of  methionic  acid  ;  the 
former  acid  differs  from  the  other  in  having  the  CH2  group  re- 

.  A'ri.v/.  I<j02,  36,  117  <V  i,-,/. 


ISOMORPHISM  85 

placed  by  the  imido-group,  NH,  which  in  many  respects  exhibits 
a  chemical  behaviour  similar  to  that  of  the  former. 

There  are  very  striking  similarities  in  the  crystalline  forms  of 
some  substances  whose  constitution  differs  as  regards  the  nature  of 
the  linking  between  certain  carbon  atoms,  the  group  .H2C — CH.2. 
being  replaced  by  .HC  — CH.,  or  by  .C  =  C. ,  as  in  the  anhydrides 
of  succinic  acid  and  malic  acid,  with  which  also  even  that  of 
itaconic  acid  is  to  be  associated.  (In  this  group  the  comparison 
with  the  imides  would  also  be  of  interest,  z>.,  the  determination  of 
the  alteration  produced  by  the  replacement  of  oxygen  by  the  imido- 
group.)  Still  more  thoroughly  known  is  the  following  series  of 
substances,  which  exhibit  a  striking  agreement  in  their  crystallo- 
graphical  characters  : — 

Dibenzyl.  Stilbene.  Tolane. 

C-Ho  .  Cfitis  Url  .  UKri=  C- .  U,-rlr. 


a 


/Hi>  •  C'gH-j  C/rl  .   GgHg  O  .  Cgllg 

Acenaphthene  and  acenaphthylene  are  similarly  related.  In 
this  connection  also  fall  to  be  considered  the  similarities  of  crystal 
form  exhibited  by  quinone  and  ^-diketohexamethylene  ;  by  phthalic 
acid  and  its  hydro-derivatives  ;  and,  finally,  by  the  salts,  esters,  and 
bromides  of  the  hydrogenated  terephthalic  acids. 

Whether  or  not,  in  the  preceding  and  similar  cases,  the 
relationships  between  the  respective  substances  are  identical 
with  those  which  are  exhibited  by  two  typically  isomorphous 
salts,  such  as  potassium  sulphate  and  rubidium  sulphate, 
can  only  be  made  out  by  further  investigation.  On  the 
other  hand,  there  is  good  reason  to  class  under  the  head  of 
isomorphism  those  cases  in  which,  within  a  large  chemical 
molecule,  two  atoms  of  a  univalent  metal  are  replaced  by  a 
single  atom  of  a  bivalent  metal  without  any  considerable 
change  of  crystal  structure,  or  those  in  which  two  atoms  of 
a  bivalent  metal  are  replaced  by  one  of  a  trivalent  and  one 
of  a  univalent  metal.  Such  replacements  are  often  observed 
— as,  for  example,  that  of  Ca  and  Na0  in  different  silicates, 
especially  those  which  are  hydrated  ;  of  Cu2  (cuprous)  and 
Pb  in  many  natural  thio-salts  ;  of  Ca2  and  AlLi  or  FeNa 
in  the  pyroxene  group  of  minerals  ;  and,  finally,  of  SiNa 
and  AICa  in  the  series  of  the  felspars.  In  the  latter  case 


86  CHEMICAL  CRYSTALLOGRAPHY 

the  two  compounds  (albite,  NaAlSi3Os,  and  anorthite, 
CaAl2SioOs)  behave  in  all  respects  like  isomorphous  sub- 
stances, in  the  closest  sense  of  the  word,  and,  in  addition, 
possess  almost  identical  equivalent  volumes. 

As  appears  from  the  introductory  considerations  at  the 
beginning  of  this  section,  the  isomorphism  of  two  substances 
depends  on  the  fact  that  the  entrance  of  the  atoms,  or  (to 
take  into  account  the  last-mentioned  relationships)  groups 
of  atoms,  which  replace  each  other  in  the  substances, 
produces  a  similar  change  in  the  crystal  structure  of  the 
compound  from  which  they  are  in  common  derived.  Since 
the  extent  of  this  change  depends  not  only  on  the  nature 
of  the  substituting  atoms  or  groups  of  atoms,  but  also  on 
that  of  the  original  substance,  it  follows  that  the  differences 
which  are  to  be  observed  in  cases  of  isomorphous  replace- 
ment by  the  same  substituents,  are  different  in  different 
isomorphous  series  ;  and  in  general  they  must  be  smaller 
the  greater  the  number  of  atoms  common  to  the  isomor- 
phous substances.  There  cannot  exist,  therefore,  any  sharp 
boundary  between  isomorphous  substances,  in  the  narrowest 
sense,  and  others  which  exhibit  morphotropic  relationships 
to  one  another ;  this  is  the  reason  why  the  idea  of 
isomorphism  cannot  be  strictly  defined,  and  attempts  have 
been  made  to  discover  other  properties,  over  and  above  the 
analogy  of  chemical  constitution  and  the  close  agreement 
of  the  crystal  structure,  which  would  allow  of  isomorphous 
substances  in  the  strictest  sense  of  the  word  being  dis- 
tinguished from  those  less  closely  related  to  one  another. 
In  this  connection  the  behaviour  of  isomorphous  substances 
towards  their  solutions  comes  especially  into  consideration. 

B.  Relations  between  Crystals  and  Solutions 
of  Isomorphous  Substances 

Episomorphism. — When  a  crystal  of  one  substance  is 
introduced  into  the  solution  of  another  substance  which  is 
isomorphous  with  it,  then,  if  the  first  substance  is  also 
soluble  in  the  solution,  there  will,  of  course,  be  partial 


ISOMORPHISM  87 

dissolution  ;  should,  however,  in  consequence  of  evapora- 
tion, a  separation  of  the  substance  originally  present  in 
the  solution  take  place,  then  the  crystal  will  grow  by  the 
parallel  accretion  of  particles  of  the  substance,  just  as  it 
would  grow  in  its  own  solution.  Thus,  an  octahedron  of 
chrome  alum  grows  in  a  solution  of  aluminium  alum,  and 
vice  versa.  In  the  latter  case,  should  the  crystal  also 
possess  cubic  faces,  then  a  much  larger  proportion  of 
chrome  alum  will  be  deposited  upon  them  in  a  given  time 
than  upon  the  octahedral  faces  ;  this  can  be  easily  observed, 
owing  to  the  dark  colour  of  the  chromium  salt.  Very  fine 
parallel  overgrowths  (episomorphs)  formed  in  this  way  from 
salts  possessing  different  colours,  were  prepared  by  K.  von 
Hauer ;  as,  for  example,  those  of  magnesium  sulphate, 
MgSO4,7H2O,  on  magnesium  chromate,  MgCrO4,7H.,O,  or 
on  nickel  sulphate,  XiSO4,7H2O  ;  of  potassium  magnesium 
sulphate,  K9Mg(SO4)0,6H0O,  on  the  corresponding  cobaltous 
and  nickel" salts,  K2Co(SO4)o,6H2O  and  K2Ni(SO4)2,6H2O. 
In  nature,  episomorphs  of  potash  and  soda  felspars  are  very 
common. 

The  behaviour  of  a  supersaturated  solution  when  it  is 
inoculated  with  a  crystal  of  some  substance  with  which  the 
solute  is  isomorphous,  is  closely  allied  to  the  phenomenon 
just  considered.  It  is  well  known  that  the  supersaturated 
solution  of  a  salt  can  be  made  to  crystallise  immediately  by 
contact  with  a  particle  of  the  solid  salt.  The  same  result 
is  attained,  however,  by  contact  with  a  crystal  of  some 
substance  which  is  isomorphous  with  the  salt  in  solution, 
as  has  been  proved  by  experiments  on  the  sulphates 
mentioned  above,  by  various  observers. 

Under  certain  circumstances  each  of  these  phenomena 
can  be  employed  as  a  means  of  recognising  isomorphism 
in  two  substances,  but  it  must  be  noted  that  there  are  cases 
of  the  regular  growjth  of  crystals  of  non-isomorphous 
substances,  closely  allied  in  character  to  episomorphs  ;  and 
further,  that  the  crystallisation  of  supersaturated  solutions  can 
also  be  induced  by  foreign  substances.  These  phenomena, 


CHEMICAL  CRYSTALLOGRAPHY 

therefore,  serve  rather  as  confirmatory  evidence  of  the 
existence  of  isomorphism  and  not  as  independent  proofs  of 
it ;  such  proof  must,  in  the  first  instance,  be  based  on  the 
recognition  of  a  close  agreement  in  crystal  structure,  as 
brought  to  light  by  the  similarity  as  regards  cohesion, 
the  values  of  the  angles,  the  phenomena  associated  with 
the  growth  and  dissolution  of  the  crystals,  as  also  by  the 
close  agreement  in  the  values  of  the  topic  parameters. 
Intimately  connected  with  the  latter,  i.e.,  with  the  close 
similarity  as  regards  distribution  in  space,  is  that  peculiarity 
which  forms  the  most  characteristic  property  of  isomorphous 
substances — the  ability,  namely,  to  mix  with  one  another 
in  varying  proportions  to  form  homogeneous  crystals. 

C.  Isomorphous  Mixtures 

When  a  solution  containing  two  or  more  isomorphous 
substances,  mixed  in  any  proportions,  is  allowed  to 
crystallise,  there  are  formed  in  it  crystals  which  likewise 
contain  the  isomorphous  substances  in  intimate  mixture. 
If  the  quantity  of  crystallised  substance  deposited  is  small 
in  proportion  to  the  quantity  of  solution,  so  that  the 
separation  produces  no  appreciable  variation  in  the  com- 
position of  the  solution,  then  the  crystals  are  homogeneous, 
possessing  the  same  composition  throughout.  This  com- 
position, like  that  of  the  solution,  does  not  necessarily 
correspond  to  any  definite  molecular  proportions  of  the 
substances  present.  In  this  respect  isomorphous  mixtures 
differ  from  the  so-called  molecular  compounds. 

The  assumption  has  been  made  by  van  't  Hoff,1  that  an 
isomorphous  mixture  of  two  substances,  A  and  B,  is  a  solid 
solution  of  A  in  B,  just  as  the  liquid  from  which  the 
crystals  separate  can  be  looked  upon  as  a  solution  of  A  in 
the  solution  of  B,  and  he  further  assumes  that  the  gas  laws 
apply  to  the  solid  solution  just  as  they  do  to  the  liquid  one. 
If  such  be  the  case,  then  equilibrium  between  the  solution 
and  the  mixed  crystals  exists  only  when  the  composition  of 

1    '/.tits.  f.  ithys,  Chem.  1890,  JJ,  322;   foitrn.  C.  S.  £8,  1044. 


ISOMORPHISM  89 

the  mixed  crystals,  expressed  in  molecular  percentage  of  A, 
bears  a  certain  ratio  to  the  composition  of  the  solution, 
similarly  expressed  ;  this  ratio  being  given  by  the  so-called 
law  of  distribution.  With  certain  provisos,  therefore,  it 
would  be  possible,  from  the  constancy  or  variability  of  this 
ratio,  to  draw  conclusions  regarding  the  molecular  nature 
of  the  substance  A  in  the  mixed  crystals  ;  and,  since  for 
isomorphous  substances  a  similar  molecular  condition  is  to 
be  assumed,  the  same  conclusions  apply  to  B.  Most  of  the 
experimental  investigations  regarding  this  subject,  carried 
out  by  Roozeboom,  Muthmann,  Fock,  etc.,  have  led  to  the 
conclusion  that  the  salts  examined  are  present  in  the  mixed 
crystals  as  simple  molecules. 

Even  although  this  method,  as  has  been  shown  more 
especially  by  Bodlander,1  is  not  capable  of  yielding  any 
unimpeachable  determination  of  the  molecular  complexity 
of  solid  substances,  the  above  result  is  nevertheless  in 
agreement  with  those  views  regarding  isomorphous 
mixtures  which,  on  the  basis  of  the  theory  of  crystal 
structure,  we  are  forced  to  adopt.  In  the  production  of 
isomorphous  mixtures  it  is  evidently  necessary  that  the 
molecules  of  the  individual  substances  present  in  the 
solution  should  be  similarly  available  for  the  formation  of 
the  crystals  forming  in  it.  Taking  into  account  the  con- 
sideration brought  forward  on  page  13  (according  to  which 
the  idea  of  molecular  weight  has  no  longer  any  definite 
significance  for  substances  in  the  crystallised  condition), 
this  may  also  be  expressed  as  follows  : — The  regular  point 
systems  which  determine  the  arrangements  of  the  atoms  in 
the  crystal  structure  remain  in  equilibrium,  even  should  the 
places  of  a  proportion  of  the  atoms  be  taken  by  atoms  of  the 
kind  which  replace  them  isomorphously.  This  equilibrium 
will  evidently  be  characterised  by  a  more  complete  stability 
the  less  the  forces  which  determine  the  crystal  structure 
differ  for  the  isomorphous  substances  present  in  the 
mixture,  i.e.t  the  smaller  the  differences  in  the  dimensions 
»  N,  [ahrb.f,  Min,  Geol,,  etc.,  1898,  Beil.-Bd.,  1?,  52, 


90  CHEMICAL  CRYSTALLOGRAPHY 

of  their  structure  units,  as  expressed  by  the  topic  para- 
meters. Further,  the  mixed  crystal  will  appear  more 
completely  homogeneous  the  greater  the  regularity  in  the 
distribution  of  the  atoms  which  replace  one  another 
isomorphously  ;  and  it  will  exhibit  properties  which,  as  a 
rule,  stand  between  those  of  the  two  substances  crystallising 
together.  In  the  case  of  an  unbroken  series  of  mixtures 
of  two  isomorphous  substances,  there  will  therefore  occur  a 
continuous  transition  of  the  properties  from  those  of  the  one 
substance  to  those  of  the  other.1 

According  to  this  view  each  component  of  an  isomorphous 
mixture  would  retain  its  own  specific  volume,  so  that 
the  volume  of  the  mixture  would  correspond  to  the 
sum  of  the  volumes  of  the  components.  That  this  is 
in  fact  the  case  has  been  shown  by  Tschermak  for  the 
mixtures  of  albite  and  anorthite,  and  by  Pettersson  for 
those  of  certain  sulphates  and  selenates.  This  subject 
was  made  the  subject  of  very  thorough  investigation  by 
Retgers,2  and  for  this  purpose  he  specially  developed  the 
method  of  density  determination  by  means  of  dense  liquids 
(page  44),  by  which  it  is  possible  to  carry  out  the  deter- 
mination with  great  accuracy  on  quite  small  crystals,  which 
are  more  easily  obtained  in  a  homogeneous  condition. 

If  d  and  d'  represent  the  densities  of  two  isomorphous 
substances,  <?„  the  volume  percentage  of  the  second 
substance  which  is  present  in  the  mixture,  and  D  the 
density  of  the  mixed  crystals,  then  the  latter  is  determined 
by  the  expression 

D -</+*,(</' -4Q/IO°i 

/>.,  in  an  isomorphous  mixture  the  variation  of  density  with 

1  Retgers  made  this  behaviour  the  basis  of  the  following  definition  of 
isomorphism :    "  Two  substances  are   really  isomorphous   only  when   the 
physical  properties  of  their  mixed  crystals  are  continuous  functions  of  their 
chemical  composition." 

2  Zeits.  f.  phys.   Chfm.  1889,  3,  497  5  4.  593  ;  1890,  5,  436  ;  6,  193  ; 
1891,  8,  6  ;  Jour*,  C.  S.  $6,  931  ;  58,  328,  1 208  ;  60,  146,  1151. 


ISOMORPHISM  91 

composition  (the  latter  being  expressed   in  percentage  by 
volume)  is  represented  by  a  straight  line. 

To  test  the  correctness  of  this  relation,  Retgers  investi- 
gated the  following  pairs  of  salts,  whose  members  differ 
sufficiently  in  density,  and  form  isomorphous  mixtures  in 
all  proportions  : 

K,S04   and   (NH4)0SO4, 
KAl(SO4).,,i2H0O  and   TlAl(SO4).,,i2H2O, 
K.,Mg(SO4)o,6H0O   and   (NH4)0Mg(SO4)~,6H0O, 
(XH4),Mg(S04).;,6H,0  and   (NH4)2Fe(SO4).2;6H,O. 

In  all  of  these  cases  it  was  observed  throughout  that, 
within  the  limits  of  experimental  error,  the  proportionality 
between  the  density  and  the  composition  of  the  mixtures 
was  that  required  by  the  preceding  equation. 

The  salts  employed  for  the  above  investigations  are  such 
as  can  form  mixtures  in  all  proportions,  and  this  of  course 
can  be  the  case  only  when  dealing  with  substances  which 
display  complete  isomorphism,  />.,  with  substances  which 
exhibit  only  slight  differences  of  crystal  structure,  not 
merely  as  regards  relative  dimensions  but  also  as  regards 
the  absolute  values,  which  involves  closely  agreeing  equiva- 
lent volumes.  A  further  condition  is  that  the  behaviour  of 
the  respective  substances  as  regards  solubility  should  not 
differ  too  widely. 

In  the  case  of  two  substances  which  can  crystallise  in 
several  polymorphous  modifications,  the  existence  of  a  con- 
tinuous series  of  isomorphous  mixtures  of  the  substances, 
entirely  free  from  gaps,  is  possible  only  if  the  stability  of 
the  corresponding  state  in  which  the  substances  crystallise 
together  should  not  be  widely  different  in  the  two  cases.  If, 
on  the  contrary,  the  temperature  intervals  for  the  stability 
of  the  individual  modifications  of  the  two  substances 
differ  so  widely  that,  under  the  conditions  ruling  during 
the  crystallisation,  the  corresponding  state  of  the  one 
substance  is  metastable,  then  as  a  rule  this  substance  can 
crystallise  along  with  the  other  in  the  form  which  is  stable 


CHEMICAL  CRYSTALLOGRAPHY 


for  it,  but  only  to  a  limited  extent.  Within  this  limited 
range,  however,  the  two  substances  form  mixtures  to  which 
the  same  general  rules  apply  as  for  complete  mixture  series  ; 
and  this  circumstance  serves  as  an  excellent  means  of 
establishing  the  dimorphism  (or  isodimorphism)  of  a  group 
of  substances  possessing  analogous  composition. 

Such  cases  also  were  first  quantitatively  investigated  by  Retgers. 
The  two  salts,  ferrous  sulphate,  FeSO4,7H.X),  and  magnesium 
sulphate,  MgSO4,7H2O,  at  first  appear  to  contradict  the  rule  stated 
on  page  74,  that  in  analogous  compounds  magnesium  and  iron 
(ferrous)  can  always  replace  each  other  isomorphously  ;  for  the 


Density 

1.90 


VH: 


l.o 


1.60 


13. 

1.:"' 


W         'iO          JO         tO        60         BO         10        80        DO       inQ% 

FlG.  5.  M- sail 


crystals  of  the  first-mentioned  salt  are  monoclinic  prismatic,  whilst 
those  of  the  other  are  rhombic  bisphenoidal.  From  aqueous 
solutions,  at  ordinary  temperature,  it  is  possible  to  obtain  mixed 
crystals  containing  up  to  54  per  cent,  of  magnesium  sulphate  and 
possessing  the  monoclinic  form  of  ferrous  sulphate.  There  must, 
therefore,  be  a  second  (a  monoclinic)  form  of  magnesium  sulphate, 
which  can  form  isomorphous  mixtures  with  ferrous  sulphate. 
There  is  a  gap  between  the  mixture  containing  54  per  cent,  and 
the  next  higher  one,  which  contains  81  per  cent,  of  the  magnesium 
salt,  intermediate  mixtures  being  unknown  ;  mixtures  from  this 
point  up  to  pure  magnesium  sulphate  exist,  and  they  exhibit  the 
rhombic  form  of  the  latter  salt.  If  the  densities  of  these  various 
mixtures  are  plotted  against  the  corresponding  percentage  com- 
positions, as  in  Fig.  5,  it  is  seen  that  the  values  lie  upon  two 
separate  and  distinct  straight  lines,  not  parallel  to  each  other.  By 
prolongation  of  the  upper  line,  the  density  of  the  assumed  mono- 


ISOMORPHISM  93 

clinic  modification  of  magnesium  sulphate  is  found  to  be  1-691,  or 
0-014  higher  that  that  of  the  rhombic  modification,  whilst  similarly 
the  rhombic  modification  of  ferrous  sulphate  would  appear  to  have 
a  density  of  1-875,  or  0-023  lower  than  that  of  the  monoclinic 
modification  ;  in  both  cases,  therefore,  the  monoclinic  modification 
is  the  denser  of  the  two.  The  fact  that  mixtures  containing  more 
magnesium  sulphate  than  ferrous  sulphate  can  still  form  mono- 
clinic  crystals,  indicates  that  the  limit  of  stability  for  this  form  of 
magnesium  sulphate  can  not  be  very  far  removed  from  the 
ordinary  temperature.  As  a  matter  of  fact,  Marignac  obtained, 
from  supersaturated  solutions  in  the  cold,  magnesium  sulphate 
crystals  which  immediately  underwent  transformation  when  they 
were  removed  from  the  solution,  and  which,  therefore,  consisted  of 
a  modification  unstable  at  ordinary  temperature.  When  measured 
approximately,  these  crystals  gave  angle  values  which  agree  very 
closely  with  those  of  ferrous  sulphate  (Marignac  assumed  the 
crystals  to  be  trigonal  because  they  exhibit  a  rhombohedral  habit, 
which  ferrous  sulphate  itself  does).  A  rhombic  form  of  ferrous 
sulphate  has  not  as  yet  been  prepared ;  this  was  to  be  expected, 
since  the  salt  crystallises  in  the  rhombic  form  only  in  mixtures 
possessing  a  marked  preponderance  of  magnesium  sulphate. 
This  case,  therefore,  is  undoubtedly  one  of  isodimorphism,  and 
the  apparent  exception  to  the  rule  of  the  isomorphous  replacement 
of  magnesium  by  ferrous  iron  is  completely  explained. 

Sodium  nitrate  is  trigonal,  and  silver  nitrate  rhombic,  but 
Retgers  prepared  mixtures  which  had  the  form  of  the  sodium 
salt,  and  contained  up  to  52-5  per  cent,  of  silver  nitrate;  from  the 
densities  of  these  he  calculated  the  value  for  the  trigonal  modi- 
fication of  silver  nitrate  present  in  them  to  be  4-19,  whilst  the 
rhombic  modification  has  a  density  of  4-35.  On  the  other  hand, 
sodium  nitrate  crystallises  rhombically  only  in  mixtures  which 
contain  a  great  excess  of  silver  nitrate.  In  agreement  herewith, 
no  rhombic  modification  of  pure  sodium  nitrate  has  as  yet  been 
obtained,  whilst  the  second  modification  (trigonal)  of  the  silver 
salt  is  formed  when  the  fused  substance  is  allowed  to  cool,  even 
though  no  sodium  nitrate  is  present  (Lehmann). 

As  has  been  shown  by  the  investigations  of  Gossner,1  particularly 
well-marked  examples  of  limited  miscibility  are  provided  by 
potassium  and  ammonium  salts,  whose  dimorphism  can  in  this 
way  be  shown  even  in  cases  of  apparently  complete  agreement 


Zeus./.  Kryst.  1903,  38,  IIO  et  seq. 


94  CHEMICAL  CRYSTALLOGRAPHY 

of  crystalline  form.  Thus,  potassium  chloride  and  ammonium 
chloride  (as  also  potassium  bromide  and  ammonium  bromide), 
which  are  cubic,  and  even  crystallise  in  the  same  symmetry  class, 
form  mixtures  only  to  a  very  limited  extent ;  on  the  one  hand 
crystals  are  obtained,  possessing  the  habit  of  the  potassium  salt, 
which  contain  only  quite  small  proportions  of  ammonium  chloride  ; 
and,  on  the  other,  crystals  with  the  habit  of  the  ammonium  salt, 
which  contain  only  quite  small  proportions  of  potassium  chloride. 
The  explanation  of  this  fact  is  that  there  exists  a  second  modifica- 
tion of  ammonium  chloride,  likewise  cubic,  which,  however,  is 
extremely  labile,  and  therefore  forms  isomorphous  mixtures  with 
the  ordinary  modification  of  potassium  chloride  (which  is  iso- 
morphous with  this  modification  of  ammonium  chloride,  and  not 
with  the  ordinary  one)  only  when  there  is  a  great  excess  of  the 
potassium  salt.  Similar  behaviour  is  exhibited  by  the  nitrates  of 
potassium  and  ammonium,  both  of  which  crystallise  rhombic,  but 
in  forms  which  cannot  without  straining  be  referred  to  each  other, 
and  which  in  fact  do  not  correspond  to  each  other.  From  mixed 
solutions  two  kinds  of  crystals  separate,  the  one  having  the  form  of 
potassium  nitrate  and  containing  little  ammonium  nitrate,  the 
other  having  the  form  of  ammonium  nitrate  and,  though  contain- 
ing larger  proportions  of  the  potassium  salt,  nevertheless  consisting 
chiefly  of  ammonium  nitrate  ;  there  is  therefore  a  considerable  gap 
in  the  series  of  mixtures. 

Cases  similar  to  the  preceding  examples  are  not  un- 
common, in  which  two  analogously  constituted  compounds, 
which  might  be  expected  to  exhibit  isomorphism,  exhibit 
certain  similarities  in  crystalline  form,  and  were  therefore 
formerly  designated  as  isomorphous.  This  was  done  even 
when  the  reference  to  a  common  fundamental  form  necessi- 
tated the  multiplication  of  the  parameters  by  J,  §,  f ,  or 
similar  factors,  so  that  the  faces  observed  on  the  crystals 
became  highly  improbable,  to  judge  from  their  symbols. 
If  two  such  substances  are  examined  as  regards  their 
miscibility,  it  is  regularly  found  that  the  one  is  able  to 
take  up  only  very  limited  quantities  of  the  other  in  iso- 
morphous admixture,  so  that  the  two  crystalline  substances 
— we  shall  designate  them  as  A1  and  B2 — regarded  as 
isomorphous  do  not  represent  corresponding  states  ;  the 


ISOMORPHISM  95 

substance  A  possesses  a  second  modification,  A2,  which  is 
really  isomorphous  with  B0,  and  therefore  forms  mixtures 
with  it,  whilst  those  mixtures  in  which  Al  preponderates 
contain  the  substance  B  in  a  second  form,  Bx,  isomorphous 
with  Aj.  The  similarity  between  the  crystalline  forms  of 
Aj  and  B2  depends  on  the  fact  that  the  two  modifications 
of  A  (and  likewise  those  of  B)  present  certain  resemblances  ; 
as  already  mentioned  on  page  34,  however,  a  closer  investi- 
gation of  such  cases  always  shows  that,  as  regards  the 
natural  fundamental  form,  the  cohesion,  etc.,  there  exist 
such  profound  differences  that  an  essentially  different 
crystal  structure  must  be  assumed  for  the  two  modifications. 

From  the  fact  that  two  substances  give  rise  to  only  the 
two  extremities  of  a  mixture  series,  it  is  therefore  safe  to 
conclude  that  they  are  isodimorphous.  The  length  of  the 
mixture  curve  at  the  one  side  or  the  other  gives,  as  the 
above  examples  have  shown,  an  indication  as  to  which  of 
the  two  unknown  modifications  possesses  the  greater  stability 
in  the  pure  state,  and  may  therefore  be  the  more  easily 
obtainable. 

Sometimes  the  mixtures  of  two  such  isopolymorphous 
substances  exhibit,  in  the  middle  part  of  the  series,  the 
form  of  a  third  modification,  in  which  neither  of  the  indi- 
vidual compounds  crystallises  when  pure. 

This  was  observed  by  Fock,1  with  the  dithionates  of  potassium 
and  thallium,  K2S2O6  and  Tl.2SoO6,  and  by  Gossner,2  with  the  acid 
sulphates  of  potassium  and  ammonium,  KHSO4  and  NH4HSO4. 
Such  phenomena  are  exceptionally  complicated  in  the  case  of 
sulphur  and  selenium  ;  ordinary  rhombic  sulphur  can  take  up  to 
35  per  cent,  of  selenium  in  isomorphous  mixture,  the  corresponding 
modification  of  selenium  being  itself  unknown  ;  there  is  no  mono- 
clinic  modification  of  selenium  corresponding  to  the  monoclinic 
sulphur  obtained  from  the  fused  substance,  and  isomorphous 
mixtures  do  not  occur ;  the  form  of  a  third  modification,  likewise 
monoclinic,  appears  also  in  mixtures  containing  from  35  to  66  per 
cent,  of  selenium  ;  another  monoclinic  form,  different  from  these* 

1  Zeits.f.  Kryst.  1882,  6,  163. 
*  Loc.  cit.  1904,  39,  381. 


!»r.  CHKMICAI,  CRYSTALLOGRAPHY 

is  exhibited  by  the  mixtures  containing  more  selenium,  and  also  by 
the  pure  selenium  crystallTsed  from  solution  in  hot  carbon 
bisulphide  ;  the  form  of  pure  selenium  crystallised  from  carbon 
bisulphide  at  ordinary  temperature,  and  that  of  "metallic" 
selenium,  are  unknown  on  pure  sulphur  and  also  on  mixtures.1 

Gaps  in  an  isomorphous  mixture  series  apparently  can  also 
arise  from  the  formation  of  the  crystals  being  disturbed  by 
the  separation  of  other  hydrates,  or  owing  to  the  fact  of  certain 
mixtures  crystallising  less  perfectly  and  therefore  being  over- 
looked during  the  investigation.2  In  such  cases  the  proof 
that  the  mixtures  belong  to  a  single  isomorphous  series  is 
supplied  by  the  fact  that  the  two  curves,  which  represent 
the  relation  between  the  density  and  the  composition,  for 
the  mixtures  actually  examined,  are  not  parts  of  two  non- 
parallel  straight  lines,  as  in  Fig.  5,  page  92,  but  are  parts  of 
one  and  the  same  straight  line.  Complete  continuity  of  the 
isomorphous  mixture  series  has  been  proved  as  yet  only  for 
a  small  number  of  pairs  of  salts,  and  these  all  exhibit  great 
similarity  of  the  two  isomorphous  salts,  as  regards  cohesion, 
greater  or  less  favouring  of  individual  forms  during  the 
formation  of  the  crystals,  etc.,  so  that  a  very  close  agreement 
of  the  crystal  structures  must  be  assumed.  It  would  there- 
fore be  appropriate,  in  order  to  avoid  arbitrariness  in  the  use 
of  the  word  "  isomorphous,"  to  designate  as  isomorphous 
only  such  substances  as  possess  the  property  of  crystallising 
together  in  all  proportions  to  form  homogeneous  mixtures 
whose  properties  are  continuous  functions  of  their  composi- 
tion. It  must  be  admitted  that,  in  the  majority  of  cases, 
the  proof  of  isomorphism  would  require  more  thorough 
investigations  than  at  present  exist.  For  example,  attempts 
should  be  made,  by  altering  the  conditions  of  crystallisation, 
to  complete  the  separate  sections  of  the  incomplete  mixture 
series  of  isodimorphous  substances,  as  represented  in  Fig.  5. 

The  question  of  the  behaviour  of  two  isomorphous  sub- 

1  Muthmann,  Zeits.f.  Kryst.  1890,  17,  336. 

-  See  Stortenbeker,  Zeiis.  f.  phys.  Chtm.   1903,  43,  629  ;  Journ.  C.  S.  84, 
ii.  470. 


ISOMORPHISM  97 

stances  on  separation  from  a  common  fused  magma  is  also 
of  importance.     In  the  first  place,  as  regards  the  solidifying 
point  of  such  magmas,  Kiister  has  found  from  investigation  of 
a  series  of  pairs  of  undoubtedly  isomorphous  substances,  that 
in  many  cases  the  solidifying  points  vary  proportionally  to 
the  molecular  composition  of  the  fused  mixture  of  the  two 
substances,  but  that  in  others  they  deviate  not  inconsiderably 
from  such  proportionality  ;  in  his  view,  the  latter  condition 
is  brought  about  by  non-homogeneous  solidification  of  the 
magma.     On  the  other  hand,  Roozeboom  has  shosvn  on 
theoretical  grounds  that  the  solidification  curve  for  two  iso- 
morphous substances  need  not  necessarily  be  a  straight  line, 
but  may  equally  well  be  a  curve  exhibiting  a  maximum  or  a 
minimum,   and   Reinders   has   experimentally   proved    the 
existence  of  the  latter  in  the  case  of  fused  mixtures  of  both 
modifications   of  mercuric   bromide   and   mercuric   iodide. 
Here  the  admixture  of  the  higher-melting  iodide   brings 
about  a  lowering  of  the  melting  point  of  the  bromide.     This 
is  also  the  case  with  other  substances,  which  do  not  stand  in 
isomorphous  relationships  with  one  another,  and  the  above- 
mentioned  laws  regarding  the  possible  solidification  curves 
of  fused  mixtures,  theoretically  deduced  by  Roozeboom,  are 
applicable  both   to  isomorphous  and   to  non-isomorphous 
substances.     From  the  form  of  the  fusion  curve,  therefore, 
no  certain  conclusion  can  be  drawn  as  to  the  relationship  of 
the  crystal  structures  of  the  two  mixed  substances.     This 
must  be  all  the  more  insisted  upon,  since  not  infrequently 
two  substances  are  described  as  isomorphous  merely  on  the 
ground  of  the  behaviour  of  fused  mixtures  of  them.     This  is 
the  case,  for  example,  as  regards  several  substances  examined 
by  Bruni,  their  crystallographical  relations  being  quite  un- 
known. 

The  difficulties  in  the  way  of  further  progress  in  this 
department  are  increased  by  the  fact  that  apparently  homo- 
geneous mixed  crystals  of  continuously  varying  composition 
are  obtainable  with  substances  whose  chemical  nature  is 
totally  different,  t.e.,  the  crystals  of  one  substance  are 


98  CHEMICAL  CRYSTALLOGRAPHY 

capable  of  taking  up  another  substance  (not  isomorphous 
with  it)  in  variable  proportions,  though  as  a  rule  only  to  a 
limited  extent,  in  a  uniformly  dilute  condition.  Here 
belong  the  numerous  colorations  of  natural  crystals  (such  as 
amethyst),  the  absorption  of  colouring  matters  by  salts  in 
the  process  of  crystallisation,  which  thereby  assume  the 
optical  properties  of  idiochromatic  substances  (e.g.,  strontium 
nitrate  with  Turkey-red),  the  mixture  of  ammonium  chloride 
with  variously  coloured  metallic  chlorides,  (ferric  chloride, 
etc.)  ;  such  cases  have  been  designated  "  anomalous  mixed 
crystals,"  and,  according  to  Johnsen,  are  to  be  looked  upon, 
from  the  standpoint  of  the  phase  rule,  as  mechanical 
mixtures  and  not  as  "solid  solutions."1 

To  the  truly  isomorphous  mixtures,  on  the  other 
hand,  must  be  reckoned  those  cases  in  which  two 
substances  which,  possessing  a  closely  agreeing  crystal 
structure  but  no  completely  analogous  chemical  con- 
stitution, form  a  continuous  series  of  homogeneous  mixed 
crystals — the  triclinic  felspars,  for  example.  The  predilection 
towards  certain  definite  mixture  ratios  in  the  series  named 
is  probably  connected  with  the  fact  that  apparently  a 
regular  distribution  of  the  two  kinds  of  atomic  groups 
provides  a  particularly  stable  equilibrium  of  the  crystal 
structure,  since  it  occurs  also  with  isomorphous  substances 
of  completely  analogous  chemical  constitution.2  The 
phenomenon  would  then  find  its  analogue  in  the  case  of 
polysymmetric  substances  in  the  formation,  at  certain 
temperatures,  of  sub-microscopic  lamellae  alternating  so 
regularly  that  the  simple  form  of  higher  symmetry 


1  This  author  has  given,  in  the  N.Jahrb.f.  Min.  1903,  2,  93  et  seq.,  an 
excellent  review  of  the  observations  regarding  this  phenomenon. 

2  Other  facts  also  support  the  view  that  a  greater  stability  of  crystal 
structure  exists  in  isomorphous  mixtures  when  the  constituents  are  present 
in  simple  molecular  proportions  ;  for  example,  the  minimal  vapour  tension 
of  such  mixtures  in  the  case  of  alums  and  of  vitriols,  as  observed  by 
Hollmann    (Zeits.  f.  phys.    Chem.    1901,    37,    193   et  sey. ;    Ctnlralbl.  f. 
Mm.  1904,  513  ;  Journ,  C.  S.  80,  ii.  436, 


ISOMORPHISM  99 

results  ;  this  likewise  points  to  the  greater  stability  of  such 
structures. 

Polymorphous  Transformations  of  Isomorphous  Mixtures 

As  the  melting  point  of  a  crystallised  substance  is 
altered  by  an  isomorphous  admixture,  such  is  also  the  case 
as  regards  the  temperature  of  transformation  into  a  poly- 
morphous modification.  Bellati  and  Lussena  found  that 
the  transition  temperature  of  potassium  nitrate  is  lowered 
by  addition  of  rubidium  nitrate  or  thallous  nitrate,  and  in 
the  latter  case  the  depression  is,  for  small  additions,  pro- 
portional to  the  amount  added  ;  Rothmund  observed  the 
same  regularity  in  the  depression  of  the  transition  tempera- 
ture of  carbon  tetrabromide  by  small  admixtures  of  tetra- 
chloride.  A  general  theory  of  the  phenomena  attending 
the  transformation  has  been  given  by  Roozeboom,1  based  on 
the  phase  rule.  One  of  the  cases  so  deduced  was  proved  by 
Reinders  in  a  comprehensive  investigation  which  he  made 
regarding  mercuric  bromide  and  iodide.  By  crystallisation 
after  fusion,  these  yield  a  continuous  series  of  isomorphous 
mixtures  of  the  yellow  (rhombic)  modification.  The 
transition  point  of  rhombic  mercuric  iodide  into  the 
tetragonal  form  lies  at  127°  ;  it  is  lowered  by  admixture 
of  mercuric  bromide,  and  this  effect  is 
represented  by  two  curves  (Fig.  6),  be- 
tween  which  there  lies  a  transition  in- 
terval, so  that  on  one  side  of  the  one 
curve  only  a  crystals  (the  red  tetragonal 
modification)  can  exist,  while  on  the 
other  side  of  the  second  curve  only 


crystals  can  exist.     The  fall  of  the  curve    HgBrs  Flo  6 
is  so  steep  that  the  corresponding  transi- 
tion point  for  the  pure  bromide  must  be  very  low  ;    as  a 
matter   of  fact,   mixtures    rich    in    bromide    remain    per- 
manently yellow  even  at  very  low  temperatures. 

The  last-mentioned  facts  contribute  considerably  towards 
1  Zeits.f.phys.  Chern.  1899,  30,  413  ;  Journ.  C.  S.  78,  ii.  132. 


100  CHEMICAL  CRYSTALLOGRAPHY 

an  explanation  of  the  relationships  existing  in  the  group 
HgCl.2 — HgBr, — HgL.  Here  we  have  to  do  with  three 
modifications  :  I,  the  tetragonal  form  of  the  red  iodide  ; 
n,  the  rhombic  one  of  the  bromide  ;  and  in,  that  of  the 
chloride,  which  is  likewise  rhombic  but  is  not  isomorphous 
with  the  preceding  one.  According  to  observations  by 
Lutschitzky,  made  in  the  author's  laboratory,  the  bromide 
appears  in  form  in.  in  isomorphous  mixtures  with  the 
chloride,  but  in  form  i.  in  mixtures  with  the  iodide  when 
the  crystals  are  rich  in  iodide  ;  hence  the  isotrimorphism 
of  the  group  is  proved. 

The  Crystalline  Forms  of  Isomorphous  Mixtures 

As  would  be  expected  from  the  agreement  in  the  sym- 
metry of  two  truly  isomorphous  substances,  mixtures  of  such 
substances  also  exhibit  the  same  symmetry  ;  hence  it  follows 
directly  that  two  isomorphous  cubic  substances  yield  mixed 
crystals  which  geometrically  are  identical  with  those  of  the 
pure  substances.  As  regards  the  faces  which  occur,  these 
are,  for  isomorphous  substances  under  the  same  conditions 
of  crystallisation,  generally  the  same,  and  likewise  therefore 
for  the  mixtures.  Should,  however,  the  individual  substances 
exhibit  a  difference  in  the  extent  to  which  they  affect  one  or 
another  form,  and,  consequently,  a  constant  difference  in  the 
habits  of  their  crystals  (which,  as  a  rule,  appears  to  be  more 
frequent  with  substances  crystallising  non-cubically),  then 
the  mixed  crystals  in  many  cases  are  of  an  intermediate 
habit.  The  mixed  crystals  of  many  isomorphous  substances 
(e.g.,  the  hydrated  sulphates  of  the  green-vitriol  type)  as  a 
rule  form  very  simple  combinations,  whilst  the  crystals  of 
the  pure  salts  are  often  richer  in  faces  ;  in  other  cases  the 
crystals  of  isomorphous  mixtures  exhibit  a  great  profusion 
of  faces  (e.g.,  those  of  epidote  and  other  minerals).  In  these 
latter  cases  we  have  to  deal  with  crystals  which,  in  addition, 
are  very  well  formed,  whilst  in  many  cases  the  mixed  crystals 
exhibit  a  less  perfect  development. 

This  latter  circumstance  gives  rise  to  a  special  difficulty 


ISOMORPHISM 


in  the  investigation  of  the  differences  exhibited  by  the  angles 
of  non-cubic  mixed  crystals,  relatively  to  the  composition  of 
the  latter.  The  first  attempt  to  investigate  the  manner  in 
which  the  crystallographical  dimensions  of  isomorphous  mix- 
tures depend  on  the  proportions  of  the  constituents  in  the 
mixture,  was  made  by  Groth,  who  employed  for  the  purpose 
the  perchlorates  and  permanganates  of  the  univalent  metals. 
The  result  was  to  show  that  the  axial  ratios  of  mixtures  of 
potassium  perchlorate  and  potassium  permanganate  do  not 
lie  between  those  of  the  pure  salts  ;  the  same  was  proved 
for  some  other  rhombic  substances,  and  it  was  therefore 
concluded  that  the  influence  of  the  isomorphous  admixture 
was  different  along  the  three  non-equivalent  axes,  and  was 
not  proportional  to  their  relative  lengths.  On  the  other 
hand,  Dufet,  on  mixtures  of  Epsom  salt  and  zinc  vitriol, 
found  the  variations  of  the  prism  angle  to  be  approximately 
proportional  to  the  ratios  in  which  the  two  salts  were 
present.  The  difference  for  the  pure  salts  amounts,  it  is 
true,  only  to  o°  37',  whilst  all  the  other  angles  of  the  two 
sulphates  differ  still  less  from  one  another,  so  that  no  safe 
conclusions  can  be  drawn  from  the  measurements  of  the 
mixed  crystals. 

Apart  altogether  from  the  fact  that  in  the  first  of  the 
above-mentioned  cases  the  mixed  crystals  examined  showed 
somewhat  considerable  variations  amongst  themselves,  and 
hence  were  not  in  all  instances  sufficiently  homogeneous, 
the  same  objection  arises  against  the  comparison  of  the 
axial  ratios  here  made  as  does  against  all  comparisons 
which  are  not  based  upon  the  topic  parameters  (see 
page  38). 

Those  views  regarding  the  crystal  structure  of  iso- 
morphous mixtures,  which  have  already  been  propounded 
as  fundamental  (compare  page  89),  would  lead  us  to  expect 
that  for  the  topic  parameters  of  such  mixtures  there  should 
exist  the  same  dependence  on  composition  which  was  found 
by  Retgers  to  hold  for  the  density.  If,  as  in  that  case,  we 
imagine  the  two  components  of  a  mixed  crystal  to  be 


(  KBM1CAL  CRYSTALLOGRAPHY 

present  in  uniform  distribution,  each  retaining  its  own 
specific  volume,  then  representing  the  topic  parameters  of 
the  first  substance  by  XP  ^u  wu  an(*  those  of  the  second 
substance  by  X'»  V^M  w-»  tne  parameters  of  an  isomorphous 
mixture  containing  a,  per  cent,  by  volume  of  the  second 
substance  would  be  given  by  the  equations  : 


to  =  toj  +  <7ro>2  —  wj       IOO. 

In  order  to  test  this  regularity  it  would  be  necessary  to 
select  two  substances  which  exhibit  the  greatest  possible 
differences  in  their  corresponding  topic  parameters,  and  of 
which,  in  addition,  mixtures  are  easily  obtainable  in  homo- 
geneous and  accurately  measurable  crystals  varying  widely 
in  composition. 

Optical  Properties  of  Isomorphous  Mixtures 

Since  the  molecular  optical  refraction  of  a  chemical 
compound  is  composed  of  the  values  for  the  equivalent 
refractions  of  the  individual  elements  of  which  the  com- 
pound is  composed,1  the  refractive  indices  of  two  isomorphous 
substances  are  always  different.  As  regards  mixtures  of  the 
two  it  is  therefore  to  be  expected,  from  what  has  already 
been  considered,  that  they  should  possess  refractive  indices 
calculable  from  those  of  their  components  by  a  formula 
analogous  to  those  assumed  above  for  the  topic  parameters. 
This  is  confirmed  by  the  observations  so  far  made  regarding 
the  optical  properties  of  isomorphous  mixtures. 

For  the  simplest  case,  that  of  singly  refracting  crystals,  there 
exists  the  investigation  of  a  mixture  series  of  potassium  alum  and 
thallium   alum  by  Fock,  from  whose  results  (as  recalculated  by 
Dufet)  it  appears  that  the  refractive  index  changes  proportionally 
with   the  composition  of  the  mixture.     According  to  Soret,  the 
same  holds  for  mixtures  of  potassium  alum  and  ammonium  alum. 
As  regards  optically  uniaxial  crystals,  mixtures  of  strontium 
1  See  more  particularly  Pope,  Journ.  C.  S.  1896,  69,   1530;  Zeils.  /. 
Kryst.  28,  113- 


ISOMORPHISM  103 

dithionate,  SrS.2O6,4H.>O,  and  lead  dithionate,  PbS2O,j,4H2O, 
exhibit,  according  to  Fock's  measurements,  a  proportionality 
between  composition  and  the  two  principal  indices  of  refraction 
(and  also  the  rotatory  power,  according  to  Bodlander). 

Finally,  as  regards  optically  biaxial  crystals,  rhombic  substances 
have  been  investigated,  especially  by  Dufet,  who  first  showed  the 
linear  dependence  of  the  three  principal  refractive  indices  on  the 
composition  in  the  case  of  isomorphous  mixtures  of  magnesium 
sulphate  with  nickel  sulphate  and  with  zinc  sulphate.  This 
dependence  is  also  shown  very  exactly  by  Lavenir's  measurements 
on  the  two  Rochelle  salts.  Since  small  differences  in  the  refractive 
indices  produce  relatively  large  differences  in  the  angles  of  the- 
optic  axes,  this  regularity  can  be  tested  more  accurately  by 
measurement  of  the  axial  angles  of  isomorphous  mixtures  ;  for  from 
the  known  refractive  indices  of  the  two  isomorphous  substances 
the  (theoretical)  values  for  any  mixture  can  be  calculated,  and  from 
these  theoretical  refractive  indices  the  appropriate  axial  angle  can 
be  deduced.  The  comparison  of  this  value  with  the  axial  angle  as 
determined  directly  on  the  mixed  crystal,  which  was  undertaken 
by  Dufet  for  the  sulphates  already  mentioned,  as  a  matter  of  fact 
showed  a  very  good  agreement ;  so  that  it  is  possible,  from  the 
axial  angle  of  a  mixture,  to  decide  as  to  the  composition  of  the 
latter.  Similar  results  were  obtained  by  Mallard  in  the  case  of  the 
sulphates  and  chromates  of  potassium  and  ammonium,  which  are 
likewise  rhombic.  With  the  latter,  as  with  Rochelle  salt,  the  case 
arises  of  the  optic  axes  of  two  isomorphous  substances  lying  in  two 
different  pinacoids.  In  the  mixture  series  there  is  therefore, 
necessarily,  first  a  gradual  diminution  of  the  axial  angle,  until,  for 
a  definite  colour,  and  with  a  definite  composition  of  the  mixture, 
the  two  axes  fall  together,  to  be  followed  by  a  reappearance  of  the 
biaxial  character  with  gradual  increase  of  the  axial  angle  in  the 
new  axial  plane  perpendicular  to  the  first. 

With  monoclinic  and  triclinic  crystals,  in  addition  to  the 
difference  in  the  refractive  indices,  there  arises  the  difference  in 
the  position  of  the  principal  vibration  directions  for  two  isomorphous 
substances,  and  this  also  may  be  considerable.  Very  complete 
investigations  of  such  cases  exist  only  as  regards  the  mixtures  of 
the  felspars,  for  which  it  has  been  found  that  there  is  a  change  in 
the  orientation  of  the  vibration  directions  which  is  proportional  to 
the  composition  of  the  mixture. 

In   all  the  above-mentioned  isomorphous  mixtures  we 


104  CHEMICAL  CRYSTALLOGRAPHY 

are  dealing  with  optically  normal  crystals.  There  also  exist 
observations,  however,  which  indicate  the  occurrence  of 
optical  anomalies  resulting  from  isomorphous  mixture. 
Thus,  Klocke  and  Brauns  observed  that  crystals  of  alum, 
which  contained  small  quantities  of  an  isomorphous  com- 
pound, exhibited  anomalous  double  refraction,  whilst 
perfectly  pure  crystals  possessed  normal  single  refraction. 
Whereas  the  optical  anomalies  in  this  case  probably  depend 
on  the  existence  of  compression  or  extension  stresses  due  to 
an  incomplete  equilibrium  of  the  heterogeneous  crystal 
structure,  in  other  cases  these  anomalies  may  quite  well  be 
only  apparent,  and  induced  by  polysynthetic  twin  structure. 


MOLECULAR   COMPOUNDS 

IN  the  preceding  section  (page  98),  it  was  mentioned  that 
isomorphous  mixtures  in  simple  stoichiometric  propor- 
tions appear  in  certain  cases  to  possess  greater  stability 
than  do  those  in  other  proportions.  Now,  the  view  regard- 
ing crystal  structure  which  has  been  here  adopted,  shows 
at  once  that  the  formation  of  a  crystal  from  two  different 
kinds  of  chemical  molecules,  even  though  these  differ  very 
slightly  from  each  other,  will  give  a  particularly  stable 
structure  when  the  molecules  take  part  in  this  formation 
in  regularly  alternating  manner  ;  since  such  a  substance 
has  as  much  right  to  the  name  of  "  molecular  compound  " 
as  to  that  of  "  isomorphous  mixture,"  it  is  evident  that 
that  view  does  not  permit  of  any  sharp  boundary  between 
the  two  ideas.  It  is  also  to  be  expected  that  the  predilec- 
tion for  definite  simple  stoichiometric  proportions  %will 
become  more  evident  the  greater  the  difference  between 
the  two  constituents  replacing  one  another  in  the  com- 
ponents of  the  mixture. 

An  example  of  two  substances  which,  in  the  narrowest  sense  of 
the  term,  are  isomorphous,  and  yet  exhibit  peculiar  points  of 
greater  stability  in  the  series  of  mixtures  which  they  form,  is 
provided  by  the  two  sulphates  of  magnesium  and  zinc,  investigated 
by  Hollmann  (see  note,  page  98). 

As  regards  isomorphism,  the  two  metals  magnesium  and  calcium 
exhibit  greater  differences  than  magnesium  and  zinc  do,  and  here 
the  predilection  for  simple  stoichiometric  proportions  appears 
much  more  strongly.  Calcite,  CaCO3,  and  magnesite,  MgCO.-?, 
must,  from  their  physical  properties  (crystalline  form,  cleavage, 


106  CHEMICAL  CRYSTALLOGRAPHY 

etc.),  still  be  described  as  isomorphous,  and  there  undoubtedly 
occur  mixtures  of  the  two  in  varying  proportions,  though  in  these,  as 
a  rule,  the  one  or  the  other  salt  preponderates  greatly  ;  in  nature, 
however,  it  is  mostly  the  double  salt,  dolomite,  CaCO:!,MgCO;!, 
which  has  been  formed,  and  that  even  in  presence  of  excess 
of  calcium  carbonate.  This  double  salt,  whilst  as  regards 
the  values  of  its  angles,  cohesion,  etc.,  it  occupies  a  position 
between  its  two  components,  nevertheless  differs  from  them  by 
possessing  lower  symmetry,  corresponding  to  the  less  symmetrical 
crystal  structure  which  results  when  this  is  considered  as  built  up 
of  alternate  molecules  of  the  two  components.  A  maximum  of 
stability  in  such  a  structure,  as  compared  with  those  in  which  the 
atoms  of  calcium  and  of  magnesium  are  present  in  different 
proportions,  should  also  betray  itself  in  determinations  of  the 
solubility — made,  for  example,  by  the  method  employed  by  Foote 
(see  note,  page  23) — by  the  occurrence  of  a  minimum  at  this  point  in 
the  series  ;  that  such  is  the  case  appears  highly  probable  from  the 
behaviour  of  dolomite  towards  acids,  as  observed  by  Haushofer  and 
others.  Precisely  similar  relationships  are  observed  regarding  the 
mixtures  of  the  metasilicates,  CaSiO.?  and  MgSiO;!,  which,  in  the 
ratio  i  :  i,  constitute  the  mineral  diopside. 

As  appears  from  the  considerations  just  adduced,  there 
are  transition  stages  between  isomorphous  mixtures  and 
molecular  compounds,  and  it  is  still  less  possible  to  draw  a 
sharp  boundary  between  molecular  compounds  and  the 
"  atomic  "  compounds.  As  is  generally  known,  the  designa- 
tion molecular  compounds  has  been  applied  to  combina- 
tions of  two  or  more  compounds  in  each  of  which,  accord- 
ing to  the  prevailing  theory  of  valency,  the  affinities  of  the 
atoms  are  already  fully  satisfied,  with  formation  of  crystal- 
lised substances;  the  term  is,  however,  merely  a  mode  of 
expressing  the  fact  that  we  are  not  in  a  position  to  explain 
the  constitution  of  these  substances.  But,  once  the 
chemical  nature  of  a  number  of  these  substances  (the 
chloroplatinates,  for  example)  had  been  shown  to  be  that 
of  salts  of  a  complex  acid,  the  frequently  suggested  prob- 
ability of  all  such  cases  being  true  atomic  compounds  has 
steadily  come  to  be  more  and  more  recognised.  To  Werner 
more  especially  is  due  the  credit  for  having,  on  the  basis  of 


MOLECULAR  COMPOUNDS  107 

geometrical  representations  (which  are,  it  is  true,  purely 
theoretical,  and  stand  in  no  relation  to  the  crystal  structures 
of  the  respective  substances),  shown  the  great  probability  of 
the  direct  union  of  the  atoms  which,  on  the  earlier 
hypothesis,  were  looked  upon  as  belonging  to  different 
molecules.  The  view  regarding  crystal  structure  which 
has  been  here  adopted  leads  to  exactly  the  same  con- 
clusion, when  it  is  applied  systematically  to  all  crystallised 
substances — when,  for  example,  the  crystal  structure  of  the 
double  salt  formed  by  one  molecule  of  zinc  chloride  with 
two  molecules  of  potassium  chloride,  corresponding  to  the 
formula  K.2ZnCl4,  is  conceived  as  consisting  of  three  inter- 
penetrating regular  point-systems,  of  which  the  first 
contains  twice,  and  the  third,  four  times,  as  many  atoms  as 
the  second.  The  manner  in  which  such  a  crystal  structure 
breaks  up  on  dissolution  must  evidently  depend  on  the 
nature  of  the  atoms  (i.e.,  on  the  nature  of  their  mutual 
union),  on  the  solvent,  the  concentration  of  the  solution, 
the  temperature,  etc.,  so  that  widely  different  kinds  of 
disintegration  are  to  be  expected  on  the  dissolution  of 
substances  of  this  kind,  and  such  is  indeed  found  to  be  the 
case.  In  like  manner,  also,  would  be  explained  the  circum- 
stance, so  frequently  observed  with  just  these  so-called 
molecular  compounds,  that  the  symmetry  of  the  crystal 
structure  stands  in  close  relation  to  the  number  of  similar 
atoms  in  the  chemical  molecule  (see  note,  page  15). 

A  particularly  interesting  example  of  the  substances 
under  consideration  is  provided  by  the  compounds  con- 
taining so-called  water  of  crystallisation,  which,  how- 
ever, as  is  well  'known,  cannot  be  separated  from  those 
containing  so-called  water  of  constitution.  If  these  also, 
in  the  crystallised  state,  are  considered  as  atomic  compounds 
(which  Werner  has  already  done  by  the  assumption  of  the 
replaceability  of  chlorine  by  water  molecules),  i.e.,  if  the 
oxygen  and  hydrogen  atoms  of  the  water  are  looked  upon 
as  constituents  of  the  crystal  structure  just  as  much  as 
the  other  atoms  are,  then  all  those  difficulties  disappear, 


108  CHKMK  AL  CRYSTALLOGRAPHY 

which  hitherto  the  differentiation  into  water  of  crystallisa- 
tion and  of  constitution  has  caused  ;  it  then  becomes 
explicable  why,  in  general,  demolition  of  the  crystal 
structure  ensues  on  loss  of  water  by  efflorescence,  and  also 
why,  in  certain  cases,  some  of  the  water  molecules  which 
result  on  efflorescence  are  liberated  only  at  definite  higher 
temperatures,  as  is  the  case,  for  example,  with  the  vitriols. 
In  the  same  way  also  an  immediate  explanation  is  supplied 
regarding  the  simple  relation  frequently  observed  between 
the  number  of  water  molecules  and  the  number  of  similar 
atoms  in  the  salt  molecule,  and,  consequently,  between  it 
and  the  symmetry  of  the  crystal  structure. 

The  whole  of  the  preceding  considerations  naturally 
apply  likewise  to  the  compounds  containing  so-called 
benzene,  alcohol,  acetone,  etc.,  of  crystallisation. 

In  the  theory  of  crystal  structure  here  adopted,  the 
possibility  is  nevertheless  not  excluded  that  the  atoms  of 
the  anhydrous  compound,  especially  when  this  is  of  high 
molecular  weight,  should  form  closer  atomic  groupings, 
between  which  the  atomic  groups  of  the  water  occupy 
positions  in  such  a  way  that,  even  after  their  removal  by 
elevation  of  the  temperature,  the  regular  structure  persists, 
though  necessarily  with  altered  physical  properties.  In 
that  case  these  water  groups  must  necessarily  be  endowed 
with  an  exceptional  mobility.  Behaviour  of  this  kind  is, 
as  a  matter  of  fact,  exhibited  by  the  zeolites,  according  to 
the  researches  of  Mallard,  G.  Friedel,  and  others  ;  the 
proportion  of  water  in  these  compounds  varies  with  the 
pressure  of  aqueous  vapour  in  the  surrounding  atmosphere, 
and,  once  removed,  the  water  is-  reabsorbed  when  the 
crystal  is  brought  into  moist  air  ;  or  it  may  be  replaced  by 
hydrogen,  hydrogen  sulphide,  ammonia,  carbonic  anhydride, 
or  alcohol.  A  similar  behaviour  was  also  observed  by  Tam- 
mann  in  the  case  of  the  hydrates  of  magnesium  platino- 
cyanide. 

In  the  crystal  structure  of  those  zeolites  which  in  com- 
position correspond  to  hydrates  of  a  felspar  silicate,  there  is 


MOLECULAR  COMPOUNDS  109 

found,  in  agreement  with  the  considerations  brought  forward 
above,  an  unmistakable  analogy  with  the  crystal  structure 
of  the  felspars.  It  is  also  possible  that  the  relationships 
which  Jaeger1  found  to  exist  between  silver  nitrate  and 
its  compounds  with  succino-nitrile,  may  be  comparable 
with  the  above.  An  influence  on  the  crystal  structure  by 
the  predominating  constituent  of  complex  compounds  is 
also  shown  in  the  case  of  the  native  basic  thiarsenites  and 
thiantimonites  of  silver  (stephanite,  polybasite,  etc.)  whose 
crystal  forms  show  close  affinity  with  those  of  the  isomorphous 
sulphides  of  silver  and  copper,  Ag2S  and  Cu2S. 

In  general,  however,  the  relationships  of  the  crystal 
structures  of  the  so-called  molecular  compounds  to  those 
of  their  components  have  not  yet  been  established,  and 
require  thorough  systematic  investigation. 

Racemic  and  Optically  Active  Compounds 

The  crystallised  racemic  substances  are  molecular  com- 
pounds which  by  solution  or  fusion  become  converted  into 
a  mixture  of  two  optical  antipodes,  and  this  mixture  is 
optically  inactive,  since  it  contains  the  two  components  in 
exactly  equal  proportions.  In  order  to  obtain  a  represen- 
tation of  the  crystal  structure  of  the  racemic  compounds,  it 
is  necessary,  first  of  all,  to  consider  that  of  optically  active 
substances,  and  this  we  shall  now  proceed  to  do. 

To  those  organic  substances  whose  solutions  possess  the 
power  of  rotating  the  plane  of  polarisation  of  light  must  be 
ascribed,  as  le  Bel  and  van 't  Hoff  have  shown,  a  chemical 
structure  such  that  the  molecules  of  the  dextro  (d.)  and  of 
the  laevo  (/.)  substance  are  mirror  images  the  one  of  the 
other,  but  are  not  superposably  alike.  Two  solid  structures 
which  stand  in  this  relation  are  said  to  be  enantiomorph. 
The  important  connection  which  exists  between  the 
enantiomorph  nature  of  the  optically  active  substances 
and  their  crystalline  form  was  first  recognised  by  Pasteur  ; 

iZeits.f.  Kryst.  1903,  37,  34 1 . 


110  CHEMICAL  CRYSTALLOGRAPHY 

it  can  be  expressed  as  follows  :  the  two  optical  antipodes 
of  an  optically  active  compound  possess  cnantiomorph  crystal 
structure.  They  therefore  exhibit  identity  of  scalar  pro- 
perties (density,  melting  point,  solubility,  heat  of  dissolution 
and  of  combustion,  etc.),  as  also  of  optical  and  other  ellip- 
soidal properties,  of  cleavage,  and  of  elasticity.  Finally, 
the  crystal  angles  of  the  two  substances  are  the  same, 
while  their  crystal  forms  stand  to  one  another  in  enantio- 
morphous  relationship.  As  a  consequence  of  the  last- 
mentioned  circumstance,  the  crystal  forms  of  an  optically 
active  substance  always  belong  to  one  of  those  symmetry 
classes  in  which  planes  of  symmetry — simple  or  compound 
— are  entirely  wanting,  i.e.,  in  the  case  of  triclinic  crystals, 
to  the  asymmetric  class ;  in  monoclinic,  to  the  sphenoidal 
class  ;  in  rhombic,  to  the  bisphenoidal  class  ;  in  trigonal, 
tetragonal,  and  hexagonal,  to  either  the  pyramidal  or  the 
trapezohedral  class  of  the  respective  systems ;  in  cubic 
crystals,  finally,  to  the  tetrahedral-pentagonal-dodecahedral 
or  the  pentagonal-icositetrahedral  class.1 

Since,  amongst  the  simple  crystal  forms  of  the  classes 
possessing  enantiomorph  symmetry,  those  with  the  simplest 
symbols  (/>.,  the  commonest  forms)  are  generally  such  that 
the  right  and  left  forms,  when  considered  from  the  purely 
geometrical  standpoint,  cannot  be  distinguished  from  one 
another,  it  frequently  happens  that  the  crystal  forms  of  two 
optical  antipodes  exhibit  apparent  identity  ;  namely,  when 
the  only  forms  which  occur  are  of  the  above-mentioned  kind 
(for  example,  combinations  of  the  prismatic  forms  of  the 
rhombic  system),  or  when  non-equivalent  faces,  such  as 
the  parallel  ones  at  the  opposite  poles  of  the  symmetry 
axis  of  a  monoclinic  sphenoidal  crystal,  appear  to  be  similar 
and  similarly  developed.  In  such  cases  the  enantio- 
morphism  can  be  recognised  only  by  the  investigation  of 
those  properties  which  alone  are  suitable  for  the  conclusive 
determination  of  the  symmetry  of  a  crystal,  i.e. ,  by  noting  the 

1  For  examples  of  these  classes,  see  the  author's  Pkysikatisckt 


MOLECULAR  COMPOUNDS  111 

occurrence  of  pyro-electric  polarity,  enantiomorphous  erosion 
figures,  or  unequal  development  of  the  non-equivalent  faces 
under  certain  conditions  of  crystal  formation. 

According  to  the  theory  of  crystal  structure  here 
adopted,  the  enantiomorphism  of  the  crystal  structures  of 
two  optical  antipodes  appears  as  a  direct  consequence  of 
the  enantiomorphism  of  their  chemical  molecules  ;  for, 
according  to  it,  the  interpenetration  of  the  regular  point- 
systems,  each  consisting  of  different  atoms,  is  such  that  the 
relative  position  of  the  atoms  is  the  same  as  in  the 
chemical  molecule.  Hence  the  crystal  structure  whose 
demolition  on  dissolution  yields  only  laevo-rotatory  mole- 
cules must  be  the  mirror  image  of  that  structure  which,  on 
dissolution,  yields  only  dextro-rotatory  molecules.  Here, 
therefore,  the  manner  of  interpenetration  of  the  point- 
systems  determines  the  absence  of  a  plane  of  symmetry 
for  the  whole  structure,  and,  therefore,  the  existence  of  two 
mirror-image  structures. 

As  Sohncke  has  shown,  a  regular  point-system  may,  how- 
ever, in  itself  be  so  constituted  that  two  enantiomorphous 
forms  of  it  are  possible — when,  namely,  it  possesses  a  right 
or  a  left  spiral  arrangement  of  the  points  ;  and,  as  is  well 
known,  the  so-called  crystal  rotation  (*>.,  the  property 
which  certain  crystals  possess  of  rotating  the  plane  of 
polarisation  of  light)  is  explicable  in  this  way.  If,  in 
an  optically  active  crystal,  the  interpenetration  of  the 
point-systems  is  such  that  the  atomic  groups  correspond- 
ing to  them,  into  which  the  crystal  structure  is  resolved 
on  dissolution,  are  incapable  of  enantiomorphism,  then  the 
solution  exhibits  no  optical  activity.  We  have  then  to 
deal  merely  with  crystal  rotation,  which  is  purely  and 
simply  a  consequence  of  the  nature  of  the  point-systems 
constituting  the  crystal  structure,  and  whose  extended 
treatment  belongs  to  the  domain  of  physical  crystallography. 

In  the  case  of  the  crystals  of  substances  which  are 
optically  active  in  solution,  however,  we  have  to  deal,  on 
the  one  hand,  with  the  so-called  molecular  rotation,  the 


112  CHEMICAL  CRYSTALLOGRAPHY 

rotation  caused  by  the  molecules  (/.£.,  by  the  mode  of  inter- 
penetration  of  the  point-systems  in  the  crystal),  and,  on  the 
other  hand,  with  the  crystal  rotation,  which  is  combined  with 
the  other  when ,  to  the  enantiomorphism  of  the  mode  of  inter- 
penetration  of  the  point-systems,  there  is  added  an  enantio- 
morphism inherent  in  these  themselves.  As  a  matter  of  fact, 
this  appears  generally  to  be  the  case  ;  and  when  the  mole- 
cular rotation,  as  obtained  either  by  direct  measurement  on 
the  amorphous  (fused)  substance  itself,  or  by  calculation  from 
the  rotatory  power  of  the  solution,  is  compared  with  the 
rotation  observed  on  the  crystals,  it  is  found  that  the  latter 
effect  is  derived  principally  from  the  crystal  rotation. 

According  to  the  investigations  of  H.  Traube,1  the  rotatory 
power  of  matico  camphor,  C^H^O,  referred  to  unit  density,  is,  for 
i  mm.,  in  the  amorphous  state,  -0-29°;  and  in  the  crystallised 
state,  -  2-07.  The  corresponding  values  for  cinchonine  antimonyl 
d-tartrate,  2(C19H._>>NoO,  SbC4H4O7),  5H2O,  are  :  +4-14°  and +  979°; 
for  zinc  hydrogen  malate,  Zn(HC4H4O5).2, 2H.2O,  the  values  are: 
-  055°  and  -  3-02°.  In  the  case  of  rubidium  rf-tartrate  the 
crystals  are  Icevo-rotatory,  aD  =  -  10-24°,  while  the  molecular 
rotation  of  the  amorphous  substance  is  +0-69°.  Since  the  latter 
possesses  the  opposite  sign,  the  actual  crystal  rotation  in  this  case 
amounts  to  -  10-93°.  Similarly,  the  rotatory  power  of  sucrose, 
CiaHjsOn,  is,  according  to  Pocklington,2  much  stronger  in  the 
crystallised  state  than  in  the  amorphous  state.  On  the  other  hand, 
the  rotatory  power  both  of  patchouli  camphor,  dgHooO,  and  of 
laurel  camphor,  C10Hj6O,  has  been  found  to  have  about  the  same 
value  as  the  molecular  rotation,  and  therefore  appears  to  result 
essentially  from  the  latter. 

In  accordance  with  the  view  developed  for  optically 
active  substances,  the  crystal  structure  of  a  racemic  carbon 
compound  is  to  be  viewed  thus  :  Since  the  "  asymmetric 
carbon  atoms,"  which  are  surrounded  by  the  other  atoms 
in  an  enantiomorphous  arrangement,  must  consequently 
possess  different  orientations,  they  necessarily  form  an 

1  7 fits.  f.  A'rv<t.  1894.  22,  50  ;   1899,  31,  624. 

-  Pkil.  Mag.  1901  [6],  2,  361  ;  Zeits.f.  Kryst.  37,  292. 


MOLECULAR  COMPOUNDS  113 

even  number  of  space  lattices,  two  at  least.  Each  of  the 
remaining  point-systems  composed  of  similar  atoms  must 
also  be  so  constituted  that  the  arrangement  of  the  one  half 
of  the  atoms  represents  the  mirror  image  of  the  arrange- 
ment of  the  other  half,  and  so  the  possibility  is  provided 
that  the  complete  structure  of  the  crystal  should  possess 
planes  of  symmetry.  The  system  of  asymmetric  carbon 
atoms  in  such  an  arrangement  would  then  bear  the  same 
relation  to  that  of  one  of  the  two  optical  antipodes  as  do 
the  point-systems,  composed  of  carbon  atoms,  in  the  crystal 
structure  of  two  substances  which  stand  in  polymeric 
relationship  to  one  another  ;  and  since,  in  two  substances 
of  the  latter  kind,  the  conditions  of  equilibrium  are  totally 
different,  an  essential  difference  of  crystal  structure  is  to 
be  expected  between  racemic  substances  and  their  optic- 
ally active  components,  notwithstanding  certain  points  of 
relationship  between  them. 

The  enantiomorph  crystals  of  optically  active  substances 
often  unite  to  form  twins,  so  that  yet  another  kind  of 
combination  of  the  two  optical  antipodes,  in  equal  quanti- 
ties, is  conceivable — that,  namely,  of  a  structure  consisting 
of  equally  thin  sub-microscopic  twin-lamellae,  alternately 
dextro  and  laevo.  Such  a  crystal  structure  would  represent 
the  complete  analogue  of  the  more  symmetric  form  of  a 
polysymmetric  substance  (page  6),  and  must  necessarily 
possess  the  same  density,  specific  heat,  melting  point,  etc., 
as  the  two  optical  antipodes  ;  and  its  crystal  form  would  differ 
from  the  forms  of  the  latter  only  by  the  symmetry  on  the 
twinning  plane,  and  by  the  equalisation  of  those  angles  which 
are  different  for  the  two  positions,  brought  about  by  the 
twin  structure.  This  case  probably  occurs  with  those  sub- 
stances which  Pope1  called  pseudo-racemic,  and  has 
explained  by  the  assumption  of  a  lamellar  twin  structure. 
According  to  Kipping  and  Pope,  the  circumstance  that  the 

1  See   Kipping  and   Pope,  Journ.  Cheni.  Soc.}  1897,  71,  989,  1899,  75, 
1 1 21  ;   Zeits.f.  Kryst.  1899.  30,  461. 

H 


114  CHEMICAL  CRYSTALLOGRAPHY 

melting  point  of  such  a  substance  does  not  always  coincide 
with  that  of  the  optically  active  components  depends  on 
the  fact  that  a  substance  which  is  pseudo-racemic  at 
ordinary  temperatures,  may,  on  heating,  become  trans- 
formed into  a  racemic  one,  and  naturally  it  then  possesses 
the  melting  point  of  the  racemic  substance.  Conversely, 
a  substance  which  is  racemic  at  ordinary  temperatures  may 
melt  as  such,  or  it  may  first  decompose  into  a  mixture  of 
the  two  active  constituents  ;  in  the  former  case  the  melting 
point  is  different  from  that  of  the  two  active  substances,  in 
the  latter  case  it  is  the  same.  This  is  simply  a  consequence 
of  the  general  dependence  on  temperature,  to  which  the 
crystal  structure  of  substances  in  general  is  subject. 

In  the  following  paragraphs  these  relationships  will  be 
explained  more  fully  by  means  of  actual  examples,  beginning 
with  substances  which  are  undoubtedly  racemic. 

Racemic  acid,  (r-)H2C4H4O,;,  crystallises  in  the  triclinic  pina- 
coidal  class,  and,  according  to  its  angles  and  cleavage,  possesses  a 
crystal  structure  which  is  quite  different  from  that  of  the  two  active 
tartaric  acids,  which  are  monoclinic  sphenoidal,  a  difference  pointed 
out  by  A.  Scacchi.1  The  densities  were  determined  by  Liebisch,-' 
who  found  :  for  racemic  acid,  D  =  1-788,  for  the  two  tartaric  acids, 
0  =  1759.  As  regards  the  salts  of  the  acids,  it  has  been  stated 
that  potassium  hydrogen  racemate,  (r-)KHC4H4O6,  and  potassium 
hydrogen  tartrate,  (^-)KHC4H4O«,  have  approximately  the  same 
axial  ratios.  Apart  from  the  facts  that  their  symmetry  is  different, 
and  that  in  the  case  of  the  former  salt  there  exist  contradictions, 
still  not  cleared  up,  between  the  determinations  made  by  Scacchi 
and  those  by  Wyrouboff,  the  two  compounds  differ  as  regards  their 
cleavage,  and  have  certainly  a  totally  different  crystal  structure. 
For  the  density  of  the  racemate,  Wyrouboff  gives  a  number  which 
agrees  exactly  with  that  of  Buignet  for  the  tartrate.  It  is  evident 
that  the  racemates  and  the  tartrates  require  further  systematic  and 
comparative  investigation. 

Aspartic  acid,  HX4H3NH2O4 ;  the  racemic  compound,  which 
is  monoclinic  prismatic,  and  the  active  ones,  which  are  rhombic 

1   I).  aciJo  paratartarico  anidro,  Alii.  A'.  Accad.}  Naples,  1869. 
-  Ann.  d.  Chem.,  1895,  286,  140. 


MOLECULAR  COMPOUNDS  115 

bisphenoidal,  exhibit  no  crystallographical  resemblances. 
(Cleavage  and  density  apparently  have  not  been  determined.) 

Malic  acid,  HoC4H4O5,  is  crystallographically  still  insufficiently 
investigated.  The  acid  ammonium  salt  of  the  racemic  acid  and 
that  of  the  active  acid  crystallise  quite  differently  ;  the  density 
is  known  in  the  case  of  the  latter  only. 

Benzoyltetrahydroquinaldine,  C10Hi...NCOCtiH.v  The  racemic 
substance  has  the  density  1-2375,  and  is  monoclinic  prismatic  ; 
the  active  one  has  the  density  1-2114,  and  is  monoclinic  sphenoidal. 
The  crystal  forms  of  the  two  exhibit  no  similarity.1 

Carvoxime,  C10H4NOH.  Both  the  racemic  and  the  active  sub- 
stances crystallise  monoclinic,  and  have  very  similar  axial  ratios, 
while  the  axial  angles  /3  show  a  greater  amount  of  discrepancy. 
The  density  of  the  former  is  1-126  ;  that  of  the  latter,  1-108  ;  the 
solubility  curves  of  the  two  are  also  different. 

Limonene  tetrabromide,  CioH1;,Br4.  In  the  form  of  the  racemic 
compound  this  substance,  formerly  called  dipentene  tetrabromide, 
has  the  melting  point  125°,  and  density  2-225,  and  crystallises 
rhombic  bipyramidal.  The  active  substance,  likewise  rhombic, 
has  a  very  similar  habit,  and  axial  ratios  which  differ  only  slightly 
from  those  of  the  former ;  the  subsidiary  forms,  as  also  the 
symmetry,  are  of  course  different.  Its  melting  point  is  104°,  and 
its  density  2-134.  An  ethereal  solution  of  equal  quantities  of  the 
active  and  inactive  substances  yields  no  mixed  crystals,  but  separate 
crystals  of  melting  points  125°  and  104°  respectively  (Wallach). 

Benzylidene  camphor,  C10H14O.CH.C6H5.  The  racemic  sub- 
stance has  the  melting  point  73°,  and  forms  monoclinic  prismatic 
crystals,  totally  different  from  the  rhombic  bisphenoidal  form  of 
the  active  components  ;  these  have  the  melting  point  98°,  and  the 
density,  within  the  limits  of  experimental  error,  agrees  with  that  of 
the  racemic  substance.2 

As  shown  by  these  and  other  examples,  racemic  sub- 
stances in  general  possess  a  crystal  structure  different  from 
that  of  the  optically  active  components,  as  is  the  case  with 
isomeric  substances  generally.  As  a  rule,  the  racemic 
substance  possesses  the  higher  density,  lower  solubility,  and 
higher  melting  point.  When  the  melting  point  coincides 

1  Pope  and  Peachey,  Journ.  C.S.  1899,  75,  1066  etseq.;  Zeit.  f.  Kryst. 
34,  612  etseq. 

-  Minguin,  Zeits.  f.  Kryst.  1904,  39,  317. 


116  CHEMICAL  CRYSTALLOGRAPHY 

with  that  of  the  active  substance,  it  is  to  be  assumed  that 
the  racemic  compound,  before  melting,  undergoes  trans- 
formation into  a  mixture  of  the  two  optical  antipodes. 

The  following  substances,  it  seems  probable,  belong  to 
the  class  of  pseudo-racemic  compounds,  in  which  the  never- 
failing  resemblance  between  their  crystal  forms  and  those  of 
their  optically  active  components  is,  as  stated  on  page  113, 
best  explained  by  the  assumption  of  a  sub-microscopic 
lamellar  structure  composed  of  equal  proportions  of  the  two 
components : 

Calcium  hydrogen  malate,  Ca(HC4H4Ot;)2,6H._,O.  When  pre- 
pared from  the  racemic  acid,  this  salt,  according  to  Pasteur,  has  the 
same  form  and  cleavage  as  the  salt  prepared  from  the  active  acid, 
only  the  hemihedral  faces  are  wanting.  Further  data  are  not 
available. 

Sobrerol,  Cl0H18O2.  When  crystallised  from  an  alcoholic  solu- 
tion of  a  mixture  of  equal  parts  of  the  two  active  substances,  this 
compound  is  rhombic,  and  its  form,  as  regards  the  axial  ratios, 
optical  properties,  habit,  and  cleavage,  is  almost  identical  with 
that  of  the  two  active  components ;  these  form  monoclinic 
sphenoidal  crystals,  and  exhibit  twinning  on  the  plane  which  is 
to  be  assumed  as  the  plane  of  polysynthetic  structure  for  the 
pseudo-racemic  rhombic  crystals.1  The  densities  of  the  rhombic 
and  of  the  monoclinic  crystals  likewise  coincide  within  the  limits 
of  experimental  error,  but  the  melting-points  are  different ;  in 
order  to  explain  this  difference,  it  must  be  assumed  that  the 
rhombic  crystals,  on  heating,  become  transformed  into  a  truly 
racemic  compound,  whose  melting  point,  naturally,  is  different  from 
that  of  the  monoclinic  crystals. 

w-Bromocamphoric  anhydride,  C10Hi3BrO;{,  has,  both  in  the 
inactive  and  in  the  optically  active  states,  the  same  crystalline 
form  and  the  same  melting  point.-' 

Bromobenzylidene  camphor,  C    ,  1 1 ,  ,l'.r( ),  when  crystallised  from 

1  Armstrong  and  Pope,  Journ.  C.  S.  1891,  59,  317  ;  Miers  and  Pope, 
Znts.f.  Kryst.  1892,  20,  321  etseq. 

-  Kipping  and  Pope,  Journ.  C.  S.  1897,  71,  1000  ;  Zeits.  /.  AVn/. 
30,  470.  The  dipentene  hydrochloride  nitrolanilide,  mentioned  at  the 
same  place,  docs  not  belong  to  this  class,  as  the  two  substances  have 
since  been  proved  to  \>c  identical,  .md  ractmir. 


MOLECULAR  COMPOUNDS  117 

equal  quantities  of  the  two  optical  antipodes,  exhibits  the  same 
forms  as  these  do,  but  lacks  the  pyramidal  faces  characteristic  of 
the  sphenoidal  hemihedrism  of  the  active  substances  ;  it  has  the 
same  density.  The  difference  of  melting  point  is  to  be  referred  to 
a  transformation,  on  heating  (but  previous  to  fusion),  of  the  pseudo- 
racemic  substance  into  a  truly  racemic  one. 

Camphorsulphonic  chloride,  C10H15O.SO.2C1,  crystallises  from  a 
mixture  of  the  two  antipodes  in  rhombic  bipyramidal  crystals, 
which,  though  they  cannot  be  completely  measured,  have  axial 
ratios  and  optical  properties  similar  to  those  of  the  two  components, 
which  form  rhombic  bisphenoids.  The  lower  melting  point  of  the 
bipyramidal  crystals  is  undoubtedly  due  to  a  transformation  into  a 
racemic  substance.1 

frans-Camphotricarboxylic  anhydride,  C^H^O,,  exhibits,  both 
in  the  active  and  in  the  inactive  states,  monoclinic  crystals  with 
similar  habit,  identical  cleavage,  and  angles  as  nearly  alike  as 
those  of  isomorphous  substances  ;  the  crystals  of  the  inactive 
substance,  however,  are  less  completely  developed,  and  exhibit 
quite  distinctly  irregularities  of  formation.  Density  and  melting 
point  are  exactly  the  same  for  both.2  With  regard  to  this  example 
(and  also  to  another  mentioned  in  the  paper  quoted),  it  must  be 
remarked,  however,  that  the  crystalline  form  of  the  inactive  sub- 
stance cannot  well  be  derived  from  that  of  the  active  substances  by 
twin  formation. 

As  appears  from  the  preceding  examples,  there  is,  as 
yet,  no  conclusive  evidence  to  show  that  the  so-called 
pseudo-racemic  substances  are  built  up  by  a  regular  sub- 
microscopic  intergrowth  of  the  two  active  components, 
though  in  many  cases  this  seems  highly  probable.  Since 
also,  as  shown  on  page  115,  substances  which  are  un- 
doubtedly racemic  may  exhibit  certain  similarities  between 
their  crystalline  forms  and  those  of  the  active  substances,  it 
would  require,  in  order  to  arrive  at  a  definite  conclusion 
a  very  thorough  investigation  of  all  the  crystallisation 
relationships  of  such  substances,  and,  above  all,  an  exact 

1  Kipping  and  Pope,  Joum.  C.  S.  1893,  63,  554  ;  1897,  71,  996;  Zeils. 
f.  R'ryst.  25,22$  et  seq.  ;  30,  467. 

-  Kipping  and  Pope,  Journ.  C.  S.  1897,  71,  986,  995  ;  /tils.  f.  A'rysf, 
1899,30,456,466. 


118  CHEMICAL  CRYSTALLOGRAPHY 

study  of  the  transformation  phenomena  exhibited  by  them  ; 
these  may  here  be  of  totally  different  kinds — such,  namely, 
as  are  caused  by  the  existence  of  polymorphous  modifica- 
tions, and  such  as  depend  on  the  transformation  of  a  mixture 
of  the  dextro  and  laevo  substances  into  the  racemic,  and  rice 
versa.  The  criteria  which  have  been  deduced  from  the 
phase  rule  by  Roozeboom,1  for  distinguishing  by  solu- 
bility and  melting  point  between  racemic  and  pseudo- 
racemic  compounds,  on  the  one  hand,  and  mechanical 
conglomerates  of  the  optical  antipodes,  on  the  other, 
are  of  importance  in  this  connection.  (See  also  Adriani's 
paper  on  the  solidification  and  transformation  phenomena 
exhibited  by  optical  antipodes.2) 

As  the  number  of  well  crystallised  substances,  concerning 
which  we  know  with  certainty  that  they  stand  mutually 
in  the  relation  of  racemic  compound  and  its  optically  active 
components,  is  steadily  increasing,  especially  by  reason  of 
the  progress  being  made  in  the  chemistry  of  the  terpenes 
there  is  no  lack  of  material  for  investigations,  which,  if 
carried  out  systematically  on  a  large  number  of  substances 
in  the  manner  indicated  above,  would  serve  to  elucidate 
finally  the  relationships  between  the  crystal  structures  of 
the  optical  antipodes  and  that  of  their  racemic  and  pseudo- 
racemic  compounds. 

1  Zeits.  /.  Phys.  Chem.  1899,  28,  494  et  seq.  ;  Journ.  C.  S.  76,  ii.  401. 
'-'  '/tits.  f.  Phys.  Chem.  1900,  33,  453  ft  seq. ;  Journ.  C.  S.  78,  ii.  462. 


INDEX 


ACETAXILIDE,  55,  59 
derivatives,  53,  55 
Acetone  of  crystallisation,  108 
Acetylene  tetrabromide,  45 
Alcohol  of  crystallisation,  108 
Alkaline  earth  metals,  isomorphism, 

71 

Alkali  metals,  isomorphism,  71 
Alkylammonium      chloroplatinates, 

48,  53 

iodides,  47 

Allotropic  modifications,  15 
Aluminium,  isomorphism,  76,  85 
Alums,  53,  77,  9* 
Amidosulphonic  acid,  64 
Ammonium  benzoate,  64 

chloroplatinate,  48,  53 

fluosilicate,  29,  32 

iodide,  47 

isomorphism,  73,  8l,  91 

nitrate,  21,  31,  32 

paratungstate,  30 

phenylglycollate,  64 

tartrate,  64 
Anomalous  melting  point,  35 

mixed  crystals,  98 
Antimonious  oxide,  31,  32 
Antimony,  isomorphism,  78,  79 
Arsenic,  31,  32,  34 

isomorphism,  78 
Arsenious  oxide,  31,  32 
Aspartic  acid,  114 
Atomic  groups,  isomorphism,  81 
/KAzoxyanisole,  27 

BARIUM,  isomorphism,  75 
UP 


Benzenesulphonic  acid,  84 
Benzene  of  crystallisation,  108 
Benzoic  acid,  56,  64,  84 
Benzophenone,  23 
Benzoyltetrahydroquinaldine,  115 
Benzylidene  camphor,  1 1 5 
Beryllium,  isomorphism,  74 

sodium  fluoride,  30 
Bismuth,  isomorphism,  78 
Boracite,  9,  31,  32,  34 
Boron,  isomorphism, '76 
Bromine,  isomorphism,  80 
Bromobenzylidene  camphor,  116 
w-Bromocamphoric  anhydride,  Il6 
Bromonitroacetanilide,  57 
l:2:4-Bromonitrophenol,  54,  67 
Bromohalogenonitrophenols,  67 
Butylammonium  chloroplatinate,  50 

CADMIUM,  isomorphism,  74 
Caesium,  isomorphism,  72 

sulphate,  68 
Calcium  carbonate,   17,  22,  31,  32, 

105 

chloral uminate,  9,  31 

hydrogen  malate,  116 

isomorphism,  75,  85 

potassium  chromate,  31 
Camphors.  112,  115 
Camphorsulphonic  chloride,  117 
/raw^-Camphotricarboxylic       anhy- 
dride, 117 
Carbamides,  51 
Carbon,  31,  32 

isomorphism,  77 

tetrabromide,  27,  32,  33 


120 


INDEX 


Carvoxime,  115 

Cerium  silicotungstate,  31 

isomorphism,  78 
Chemical  isomerism,  3,  4,  14 
/-Chloracetanilide,  55 
Chlorine,  isomorphism,  80 
Chlorobenzoic  acids,  56 
Chloronitrobenzoic  acids,  56 
Chloroplatinates,  9,  30,  31,  32,  48 
Chromium,  isomorphism,  69,  77,  79 
Cinchonine  antimonyl  tartrate,  112 
Cobalt,  isomorphism,  74,  77 
Coloured  crystals,  98 
Copper,  isomorphism,    73.    74,    76, 

85 

Corresponding  states,  36 
Crystal  molecule,  12,  13 
rotation,  in 
structure,  I 

theory  of,  12 

unit  of,  13 

Crystallisation  microscope,  4 
Cubic  space  units,  42 
Cupric  nitrate,  basic,  30 
Cyanogen  compounds,  isomorphism, 

82 

DENSITY  determination,  44 
w-Diamidobenzene  sulphonic  acid, 30 
Dibenzyl,  85 
/-Dibromobenzene,  58 
o-/-Dichloracetanilide,  55 
Dimethylammonium   chloroplatin- 

ate,  30,  49 

Dimethylcarbamides,  51,  52 
Dimorphism,  see  Polymorphism 
Dinitrobenzene,  61 
Dinitrobenzoic  acids,  60 
DinitrodiphenylcarbamMe,  29 
Dinitrophenols,  61 
Diopside,  106 
Dipropylammonium  chloroplatinate, 

31 
Dithionates,  95,  103 


Dolomite,  75,  106 
Double  salts,  106,  107 

ELEMENTS,  crystal  structure  of,  14 
Enantiomorphism  of    optical    anti- 
podes, 109 

Enantiotropic  substances,  26 
Episomorphism,  86 
Episomorphs,  87 
Equivalent  volume,  39 
Ethylammonium  chloroplatinate,  49 

FELSPARS,  7,  85,  87 
Ferrous  sulphate,  92 
Fluorine,  isomorphism,  71,  80 
Fluosilicates,  29,  32 
Formanilide  derivatives,  $2 
Freezing    points     of     isomorphous 
mixtures,  97 

GALLIUM,  isomorphism,  77 

Gerhardtite,  30 

Glaserite,  8 

Glucinum,  see  Beryllium 

Glutamic  acid,  64 

Gold,  isomorphism,  73 

II.VLOGENO-DERIVATIVES,  34 

isopolymorphism,  70 
Halogens,  isomorphism,  80 

morphotropic  effect,  54 
Heavy      metals,      univalent,      iso- 
morphism, 71 

Heptaparallelohedron,  41,  42 
Hexachlorethane,  20,  32 
Hexachloroketodihydrobenzene,  17, 

28 

Hexagonal  space  units,  43 
Hexaparellelohedron,  41,  42 
Homologous  substances,  52 
Hydrates,  107 

Hydroquinone  derivatives,  68 
Hydroxyl,  isomorphism,  82 

morphotropic  effect,  6 1 


INDEX 


121 


ICE,  3  note 

Imidosulphonates,  84 

Indium,  isomorphism,  77 

Iodine  compounds,  dimorphism,  34, 

70 

isomorphism,  80 
Iridium,  isomorphism,  77 
Iron,  isomorphism,  74,  77,  85,  91 

vitriol,  92 

Isodimorphism,  see  Isopolymorphism 
Isomerism,  chemical,  3,  4,  14 

physical,  3,  4 

Isomorphism,  37,  66,  69,  90  note 
Isomorphous  mixtures,  88,  105 

crystal  forms  of,  100 

densities,  90 

optical  properties,  102 

polymorphous  transformations, 

99 

solidification  curves,  97 

vapour  pressures,  98  note 
Isomorphous   overgrowths,  see  Ep- 

isomorphs 

Isopolymorphism,  70,  92,  95 
Isopropylammonium     chloroplatin- 

ate,  9,  50 

KLEIN'S  solution,  45 

LABILE,  state,  17 
Laurel  camphor,  112 
Lead  dithionate,  103 

isomorphism,  75,  76,  78,  85 
Leucite,  10,  34 
Limonene  tetrabromide,  115 
Lithium  ammonium  sulphate,  10 

isomorphism,  71,  85 

potassium  sulphate,  10 

MAGNESIUM,  isomorphism, 74, 91, 92 

platinocyanide,  108 
Malate,  calcium  hydrogen,  116 

zinc  hydrogen,  1 1 2 
Malic  acid,  115 


Manganese,  isomorphism,  74,  77 
Mannitol,  30,  33 
Matico  camphor,  112 
Melting  point,  anomalous,  33 
Mercuric  halides,  isotrimorphism,  99 

iodide,  19 

Mercury,  isomorphism,  76 
Metastable  state,  16 
Methionic  acid,  84 
Methyl,  morphotropic  effect,  53 
Methylammonium     chloroplatinate, 

48 

Methylcarbamides.  51 
Methylene  iodide,  45 
Microscope,  crystallisation,  4 
Mimetic  forms,  6 
Mirror  image  forms,  109 
Mixed    crystals,    see    Isomorphous 

mixtures 
anomalous,  98 
Modifications,  2,  34 
Molecular  compounds,  88,  105,  106 

rotation,  in 

volume,  39 

Molecule,  crystal,  12,  13 
Molybdenum,  isomorphism,  80 
Monoclinic  space  units,  40 
Monotropic  substances,  26 
Morphotropy,  36,  44 

NAPHTHALENE,  62 

sulphonic  acid  esters,  53 
Naphthols,  62 
Nickel,  isomorphism,  74,  76 
Niobium,  isomorphism,  79 
w-Xitraniline,  52 
Nitroacetanilides,  57,  59 
Nitro-/-azotoluenes,  61 
Nitrobenzoic  acids,  56,  59,  62 
Nitrogen,  isomorphism,  78 
Nitro-group,    morphotropic     effect, 

57 

/-Nitrophenol,  33 
i:2:4-Xitrotoluidine,  52 


\'2'2 


INDEX 


OPTICAL  anomalies,  104 

properties   of    isomorphous    mix- 
tures, 102 
Optically  active  compounds,  109 

crystals,  7,  II 
Ostwald's  rule,  2O,  24 
Oxygen,  isomorphism,  79 

PALLADIUM,  isomorphism,  76,  78 
Partial  isomorphism,  52 
Patchouli  camphor,  112 
Phenacetnric  acid  esters,  53 
Phenol,  3  note 
Phenylglycollic  acid,  64 
Phenylpropionic    acid,    derivatives, 

68 
Phosphorus,  31,  32,  34 

isomorphism,  78 
Phthalates,  65,  66,  67 
Phthalic  acid,  65,  66,  83 
Physical  isomerism,  3,  4 
Picric  acid,  62,  64 
Platinum  metals,  isomorphism,  76, 

77,78 

Point  systems,  12 
Polymorphism,  3,  4,  11,  14,  16 
Polysymmetry,  5,  7,  11 
Potassium  amidosulphonate,  64 

calcium  chromate,  31 

chromate,  69 

felspar,  7 

fluosilicate,  32 

hydrogen  racemate,  114 
tartrate,  114 

isomorphism,  72,  91 

picrate,  64 

selenate,  69 

sodium  chromate,  8 
sulphate,  8 

sulphate,  10,  13,  68 

zinc  chloride,  107 

Pressure,  influence  on  equilibrium 
and  on  transition  point,  3  note, 
8,  26 


Propylammonium  chloroplatinate,5O 

chlorostannate,  50  note 
Pseudo-hexagonal  space  units,  43 
Pseudo-racemic  compounds,  113 
Pseudo-symmetric  crystal  forms,  5, 

43 
Pyroxene  group,  10 

QUARTZ,  7,  3i,  33 

RACEMIC  acid,  114 

compounds,  109,  112 
Radicals,  isomorphism,  81,  82 
"  Rare  earth"  metals,  isomorphism, 

77 

Rate  of  transformation,  17,  19,  28 
Rhodium,  isomorphism,  77 
Rhombic  space  units,  41 
Rhombohedral  space  units,  42 
Rohrbach's  solution,  45 
Rotation    of  plane   of   polarisation, 

7,  10,  109 
Rubidium  bichromate,  30 

isomorphism,  72 

sulphate,  68 

tartrate,  112 
Ruthenium,  isomorphism,  76 

SALICYLIC  acid,  62 
Santonic  acid  esters,  53 
Selenates     of    alkali     metals,     iso- 
morphism, 68 
Selenium,  isomorphism,  79 

isopolymorphism,  95 
Silicon,  isomorphism,  77,  85 
Silico-tungstate,  cerium,  31 
Silico-tungstic  acid,  71 
Silver  iodide,  31,  32 

isomorphism,  73,  93 

nitrate,  compounds  with  succino- 
nitrile,  109 

thiosalts,  109 
Sobrerol,  116 


INDEX 


123 


Sodium  beryllium  fluoride,  30 

dihydrogen  phosphate,  22 

hydrogen  glutamate,  64 
phthalate,  65 

isomorphism,  71,  85,  93 

magnesium  uranylacetate,  8 
Solid  solution?,  12,  88 
Solidification  curves,  97 
Solutionsofisomorphous  substances, 

S6 

Space  units,  38 
Specific  gravity,  see  Density 

volume,  21 
Stilbene,  85 
Strontium  dithionate,  102 

isomorphism,  75 

Structure,  theory  of  crystal,  I,  12 
Sucrose,  112 

Sulphates    of    alkali     metals,    iso- 
morphism, 68 
Sulphoacetic  acid,  84 
t'-Sulphobenzoic  acid,  84 
Sulphur,  17,  24,  25,  27,  32,  95 

isomorphism,  79 

TANTALUM,  isomorphism,  79 

Tartaric  acid,  64,  114 

Tartrate,  cinchonine  antimonyl,  112 

potassium  hydrogen,  1 14 

rubidium,  112 
Tautomeric  substances,  5 
Telluric  acid,  28 
Tellurium,  isomorphism,  78 
Temperature,   influence   on   equili- 
brium, 2 

Tetraethylammonium  iodide,  47 
Tetragonal  space  units,  41 
Telramethylammonium    chloropla- 
tinate,  49,  53 

iodide,  47 
Tetrapropylammonium  iodide,  48 


Thallium,  isomorphism,  73,  77,  91 
Thorium,  isomorphism,  78 
Thoulet's  solution,  45 
Tin,  32 

isomorphism,  76,  78 
Titanium,  isomorphism,  77,  78 
Tolane,  85 

Topic  parameters,  39 
Transformation,  2,  16,  99 

rate  of,  17,  19,  28 
Transition  point,  ti,  16,  24 
Tribromotoluenes,  57 
Triclinic  space  units,  40 
Tridymite,  31,  33 
Trinitrobenzene,  58,  62 
Trinitrobenzoic  acid,  60 
Trinitrophenol,  62,  64 
Tungstate,  ammonium  para-,  30 
Tungsten,  isomorphism,  80 
Triparallelohedron,  41 
Twin  lamellae,  6 

UNIT  of  crystal  structure,  13 

space,  38 

Uranium,  isomorphism,  78 
Uranylacetate,  sodium  magnesium, 

B 


Urea,  see  Carbamide 


VANADIUM,  isomorphism,  75,  77, 79 
Vapour-pressure  curves,  24 
Vitriols,  23 

WATER  of  crystallisation,  107 
constitution,  107 

ZEOLITES,  108 

Zinc,  isomorphism,  74 

hydrogen  malate,  112 

potassium  chloride,  107 
Zirconium,  isomorphism,  78 


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Edinburgh 


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Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish Svo,  3  oo 

Salkowski's  Physiological  and  Pathological  Chemistry.  ('Orndorff. ' Svo,  2  50 

Schimpf's  Text-book  of  Volumetric  Analysis i2rno,  2  50 

Essentials  of  Volumetric  Analysis i2mo,  i  25 

Spencer's  Handbook  for  Chemists  of  Beet-sugar  Houses i6mo,  morocco,  3  oo 

Handbook  for  Sugar  Manufacturers  and  their  Chemists  i6mo,  morocco,  2  oo 

Stockbridge's  Rocks  and  Soils .  .  Svo,  2  50 

*  Tollman's  Elementary  Lessons  in  Heat Svo,  i   50 

Descriptive  General  Chemistry Svo,  3  oo 

Treadwell's  Qualitative  Analysis.  (HalL) Svo,  3  oo 

Quantitative  Analysis.  (Hall.) Svo,  4  oo 

lurneaure  and  Russell's  Public  Water-supplies Svo,  5  oo 

Van  Deventer's  Physical  Chemistry  for  Beginners.  (Boltwood.  > i2mo,  i  50 

*  Walke's  Lectures  on  Explosives .  .Svo,  4  oo 

Washington's  Manual  of  the  Chemical  Analysis  of  Rocks Svo,  2  oo 

Wassermann's  Immune  Sera :  Haemolysins,  Cytotoxins,  and  Precipitir.s.    ;  Bol- 
duan.)   i2mo,  i  oo 

Well's  Laboratory  Guide  in  Qualitative  Chemical  Analysis Svo,  i  50 

Short  Course  in  Inorganic  Qualitative  Chemical  Analysis  for  Engineering 

Students i2mo,  i  50 

Text-book  of  Chemical  Arithmetic.     <  In  press. ) 

Whipple's  Microscopy  of  Drinking-water Svo,  3  50 

Wilson's  Cyanide  Processes i2mo,  i   50 

Chlorination  Process I2mo,  i  50 

Wulling's    Elementary    Course    in  Inorganic,  Pharmaceutical,  and  Medical 

Chemistry i2mo,  2  oo 

CIVIL  ENGINEERING. 

BRIDGES    AND    ROOFS.       HYDRAULICS.       MATERIALS    OF    ENGINEERING. 
RAILWAY  ENGINEERING. 

Baker's  Engineers'  Surveying  Instruments i2mo,  3  oo 

Bixby's  Graphical  Computing  Table Paper  19*     24}  inches.         25 

**  Burr's  Ancient  and  Modern  Engineering  and  the  Isthmian  Canal.       Postage, 

27  cents  additional.) Svo,  3  50 

Comstock's  Field  Astronomy  for  Engineers Svo,  2  50 

Davis's  Elevation  and  Stadia  Tables .  .  .Svo,  i  oo 

Elliott's  Engineering  for  Land  Drainage i2mo,  i  50 

Practical  Farm  Drainage i2mo,  i  oo . 

Fiebeger's  Treatise  on  Civil  Engineering.     (In  press.) 

Folwell's  Sewerage.     (Designing  and  Maintenance. > Svo,  3  oo 

Freitag's  Architectural  Engineering.     2d  Edition,  Rewritten Svo,  3  50 

French  and  Ives's  Stereotomy  Svo,  2  50 

Goodhue's  Municipal  Improvements.  .  .  I2mo,  i  75 

Gnodrich's  Economic  Disposal  of  Towns'  Refuse.  ......  Svc,  3  50 

Gore's  Elements  of  Geodesy.  ...  Svo,  2  50 

Hayford's  Text-book  of  Geodetic  Astronomy Svo,  3  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,  2  50 

5 


Howe's  Retaining  Walls  for  Earth 12010,  i  25 

Johnson's  (J.  B.)  Theory  and  Practice  of  Surveying Small  8vo,  4  oo 

Johnson's  (L.  J.)  Statics  by  Algebraic  and  Graphic  Methods 8vo,  2  oo 

Laplace's  Philosophical  Essay  on  Probabilities.     (Truscott  and  Emory.) .  i2mo,  2  oo 

Mahan's  Treatise  on  Civil  Engineering.     (1873.)     (Wood.) 8vo,  5  oo 

*  Descriptive  Geometry 8vo,  i  50 

JCerriman's  Elements  of  Precise  Surveying  and  Geodesy 8vo,  2  50 

Elements  of  Sanitary  Engineering 8vo,  2  oo 

Merriman  and  Brooks's  Handbook  for  Surveyors i6mo,  morocco,  2  oo 

Hugent's  Plane  Surveying 8vo,  3  50 

•Ogden's  Sewer  Design i2mo,  2  oo 

Patton's  Treatise  on  Civil  Engineering 8vo  half  leather,  7  50 

Reed's  Topographical  Drawing  and  Sketching 4to,  5  oo 

Rideal's  Sewage  and  the  Bacterial  Purification  of  Sewage 8vo,  3  50 

Siebert  and  Biggin's  Modern  Stone-cutting  and  Masonry 8vo,  i  50 

Smith's  Manual  of  Topographical  Drawing.     (McMillan.) 8vo,  2  50 

Sondericker's  Graphic  Statics,  with  Applications  to  Trusses,  Beams,  and  Arches. 

8vo,  2  oo 

Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced 8vo,  5  oo 

*  Trautwine's  Civil  Engineer's  Pocket-book :6mo,  morocco,  5  oo 

Wait's  Engineering  and  Architectural  Jurisprudence 8vo,  6  oo 

Sheep,  6  50 

Law  of  Operations  Preliminary  to  Construction  in  Engineering  and  Archi- 
tecture  8vo,  5  oo 

Sheep,  5  50 

Law  of  Contracts 8vo,  3  oo 

Warren's  Stereotomy — Problems  in  Stone-cutting 8vo,  2  50 

"Webb's  Problems  in  the  Use  and  Adjustment  of  Engineering  Instruments. 

i6mo,  morocco,  i  25 

*  Wheeler's  Elementary  Course  of  Civil  Engineering 8vo,  4  oo 

Wilson's  Topographic  Surveying 8vo,  3  50 

BRIDGES  AND   ROOFS. 

Boiler's  Practical  Treatise  on  the  Construction  of  Iron  Highway  Bridges.  .8vo,  2  oo 

*  Thames  River  Bridge 4to,  paper,  5  oo 

Burr's  Course  on  the  Stresses  in  Bridges  and  Roof  Trusses,  Arched  Ribs,  and 

Suspension  Bridges 8vo,  3  50 

Burr  and  Falk's  Influence  Lines  for  Bridge  and  Roof  Computations.  .  .  .8vo,  3  oo 

Du  Bois's  Mechanics  of  Engineering.     Vol.  II Small  4to,  10  oo 

Foster's  Treatise  on  Wooden  Trestle  Bridges 4to,  5  oo 

Fowler's  Ordinary  Foundations 8vo,  3  50 

Greene's  Roof  Trusses 8vo,  i  25 

Bridge  Trusses 8vo,  2  50 

Arches  in  Wood,  Iron,  and  Stone 8vo,  2  50 

Howe's  Treatise  on  Arches 8vo,  4  oo 

Design  of  Simple  Roof-trusses  in  Wood  and  Steel 8vo,  2  oo 

Johnson,  Bryan,  and  Turneaure's  Theory  and  Practice  in  the  rrsipr  irg  of 

Modern  Framed  Structures Small  4to,  10  oo 

Merriman  and  Jacoby's  Text-book  on  Roofs  and  Bridges : 

Part  I.     Stresses  in  Simple  Trusses 8vo,  2  50 

Part  II.     Graphic  Statics 8vo,  2  50 

Part  III.     Bridge  Design 8vo,  2  50 

Part  IV.     Higher  Structures 8vo,  2  50 

If  orison's  Memphis  Bridge.  .  .                                          4to,  10  oo 

WaddelPs  De  Pontibus,  a  Pocket-book  for  Bridge  Engineers.  .  i6mo,  morocco,  3  oo 

Specifications  for  Steel  Bridges i2mo,  i  25 

Wood's  Treatise  on  the  Theory  of  the  Construction  of  Bridges  and  Roofs.  .8vo,  2  oo 
Wright's  Designing  of  Draw-spans: 

Part  I.     Plate-girder  Draws.  .  .                                       8vo,  2  50 

Part  II.     Riveted-truss  and  Pin-connected  Long-span  Draws 8vo,  2  50 

Two  parts  in  one  volume 8vo,  3  50 


HYDRAULICS. 

Bazin's  Experiments  upon  the  Contraction  of  the  Liquid  Vein  Issuing  from 

an  Orifice.     (Trautwine.) 8vo,  2  oo 

Bovey's  Treatise  on  Hydraulics 8vo,  5  oo 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

Diagrams  of  Mean  Velocity  of  Water  in  Open  Channels payer,  i  50 

Coffin's  Graphical  Solution  of  Hydraulic  Problems i6mo,  morocco,  2  50 

Flather's  Dynamometers,  and  the  Measurement  of  Power 12010,  3  oo 

Folwell's  Water-supply  Engineering 8vo,  4  oo 

Frizell's  Water-power 8vo,  5  oo 

Fuertes's  Water  and  Public  Health i2mo,  i  50 

Water-filtration  Works i2mo,  2  50 

Ganguillet  and  Kutter's  General  Formula  for  the  Uniform  Flow  of  Water  in 

Rivers  and  Other  Channels.     (Hering  and  Trautwine.).  • 8vo  4  oo 

Hazen's  Filtration  of  Public  Water-supply 8vo,  3  oo 

Hazlehurst's  Towers  and  Tanks  for  Water-works 8vo,  2  50 

Herschel's  115  Experiments  on  the  Carrying  Capacity  of  Large,  Piveted,  Metal 

Conduits 8vo,  2  oo 

Mason's  Water-supply.     (Considered  Principally  from  a  Sanitary  Standpoint.) 

8vo,  4  oo 

Merriman's  Treatise  on  Hydraulics 8vo,  5  oo 

*  Michie's  Elements  of  Analytical  Mechanics 8vo,  4  oo 

Schuyler's   Reservoirs   for   Irrigation,   Water-power,   and    Domestic    Water- 
supply Ltis*  8vo,  5  oo 

**  Thomas  and  Watt's  Improvement  of  Rivers.     (Post.,  44C.  additional.)  4to,  6  oo 

Turneaure  and  Russell's  Public  Water-supplies ?vo,  5  oo 

Wegmann's  Design  and  Construction  of  Dams 4to,  5  oo 

Water-supply  of  the  City  of  New  York  from  1658  to  1895 4to,  10  oo 

Wilson's  Irrigation  Engineering .  .Small  8vo,  4  oo 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  3  oo 

Wood's  Turbines 8vo,  2  50 

Elements  of  Analytical  Mechanics 8vo,  3  oo 

MATERIALS  OF  ENGINEERING. 

Baker's  Treatise  on  Masonry  Construction .  .8vo,  5  oo 

Roads  and  Pavements 3vo,  5  oo 

Black's  United  States  Public  Works ObJong  4*0,  5  oo 

Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vc,  7  50 

Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering 8vo,  7  50 

Byrne's  Highway  Construction 8vo,  5  oo 

Inspection  of  the  Materials  and  Workmanship  Employed  in  Construction. 

i6mo,  3  oo 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

Du  Bois's  Mechanics  of  Engineering.     Vol.  I.  .                         Small  4to,  7  50 

Johnson's  Materials  of  Construction .Large  8vo,  6  oo 

Fowler's  Ordinary  Foundations 8vo,  3  50 

Keep's  Cast  Iron 8vo,  2  50 

Lanza's  Applied  Mechanics .  .8vo,  7  50 

Marten's  Handbook  on  Testing  Materials.     (Henning.  t     2  vols 8vo,  7  50 

Merrill's  Stones  for  Building  and  Decoration 8vo,  5  oo 

Merriman's  Text-book  on  the  Mechanics  of  Materials 8vo,  4  oo 

Strength  of  Materials i2mo,  i  oo 

Metcalf's  Steel.     A  Manual  for  Steel-users 12010,  2  oo 

Patton's  Practical  Treatise  on  Foundations 8vo,  5  o« 

Richardson's  Modern  Asphalt  Pavements.      (In  press.) 

Richey's  Handbook  for  Superintendents  of  Construction i6mo,  mor.,  4  oo 

Rockwell's  Roads  and  Pavements  in  France. i2mo,  i  23 

1 


Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Smith's  Materials  of  Machines .  i2mo,  i  oo 

Snow's  Principal  Species  of  Wood 8vo,  3  50 

Spalding's  Hydraulic  Cement i2mo,  2  oo 

Text-book  on  Roads  and  Pavements. i2mo,  2  oo 

Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced 8vo,  5  oo 

Thurston's  Materials  of  Engineering.     3  Parts.                                              .    8vo,  800 

Part  I.     Non-metallic  Materials  of  Engineering  and  Mctal.urry 8\o,  2  oo 

Part  II.     Iron  and  Steel 8vo,  3  50 

Part  III.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,  2  50 

Thurston's  Text-book  of  the  Materials  of  Construction 8vo,  5  oo 

Tillson's  Street  Pavements  and  Paving  Materials 8vo,  4  oo 

Waddell's  De  Pontibus.    (A  Pocket-book  for  Bridge  Engineers.)      i6mo,  mor.,  3  oo 

Specifications  for  Steel  Bridges.  . i2mo,  i   25 

Wood's  (De  V.)  Treatise  on  the  Resistance  of  Materials,  and  an  Appendix  on 

the  Preservation  of  Timber 8vo,  2  oo 

Wood's  (De  V.)  Elements  of  Analytical  Mechanics 8vo,  3  oo 

Wood's  (M.  P.)  Rustless  Coatings:    Corrosion  and  Electrolysis  of  Iron  and 

Steel 8vo,  4  oo 

RAILWAY  ENGINEERING. 

Andrew's  Handbook  for  Street  Railway  Engineers 3x5  inches,  morocco,  i   25 

Berg's  Buildings  and  Structures  of  American  Railroads 4to,  5  oo 

Brook's  Handbook  of  Street  Railroad  Location i6mo,  morocco,  i   50 

Butt's  Civil  Engineer's  Field-book i6mo,  morocco,  2  50 

Crandall's  Transition  Curve i6mo,  morocco,  i   50 

Railway  and  Other  Earthwork  Tables 8vo,  i   50 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book     i6mo,  morocco,  5  oo 

Dredge's  History  of  the  Pennsylvania  Railroad:    (1879) Paper,  5  oo 

*  Drinker's  Tunnelling,  Explosive  Compounds,  and  Rock  Drills. 4to,  half  mor.,  25  oo 

Fisher's  Table  of  Cubic  Yards Cardboard,  25 

Godwin's  Railroad  Engineers'  Field-book  and  Explorers'  Guide.      i6mo,  mor.,  2  50 
Howard's  Transition  Curve  Field-book.  .                                     .  .  i6mo,  morocco,  i   50 
Hudson's  Tables  for  Calculating  the  Cubic  Contents  of  Excavations  and  Em- 
bankments                                                                                8vo,  i   oo 

Molitor  and  Beard's  Manual  for  Resident  Engineers.  .                        i6mo,  i   oo 

Nagle's  Field  Manual  for  Railroad  Engineers.  ......                   i6mo,  morocco,  3  oo 

Philbrick's  Field  Manual  for  Engineers.  ...                                   i6mo,  morocco,  3  oo 

Searles's  Field  Engineering.  .                                                             i6mo,  morocco,  3  oo 

Railroad  Spiral.  .  .  .                                                                      i6mo,  morocco,  i   50 

Taylor's  Prismoidal  Formulze  and  Earthwork .8vo,  i   50 

*  Trautwine's  Method  of  Calculating  the  Cube  Contents  of  Excavations  and 

Embankments  by  the  Aid  of  Diagrams 8vo,  2  oo 

The  Field  Prac'ice  of  Laying  Out  Circular  Curves  for  Railroads. 

i2mo,  morocco,  2  50 

Cross-section  Sheet Paper,  25 

Webb's  Railroad  Construction.  ...                                                   i6mo,  morocco,  5  oo 

Wellington's  Economic  Theory  of  the  Location  of  Railways Small  8vo,  5  oo 

DRAWING. 

Barr's  Kinematics  of  Machinery.  .                       .8vo,  2  50 

*  Bartlett's  Mechanical  Drawing .8vo,  3  oo 

Abridged  Ed 8vo,  i   50 

Coolidge's  Manual  of  Drawing 8vo,  paper  i.  oo 

v.e  and  Freeman's  Elements  cf  G:~cr~!  Drafting  for  Mechanical  Enpi 

neers Oblong  4to,  2  50 

Durley's  Kinematics  of  Machines.  .  .                                                                     8v<>,  j  on 

Emch's  Introduction  to  Projective  Geometry  and  its  Applications 8vo.  2  50 

8 


Hill's  Text-book  on  Shadae  and  Shadows,  and  Perspective 8vo,  2  oo 

Jamison's  Elements  of  Mechanical  Drawing 8vo,  2  50 

Jones's  Machine  Design: 

Part  I.     Kinematics  of  Machinery 8vo,  i   50 

Part  II.     Form,  Strength,  and  Proportions  of  Parts 8vo,  3  co 

MacCord's  Elements  of  Descriptive  Geometry 8vo,  3  oo 

Kinematics;   or,  Practical  Mechanism 8vo,  5  oo 

Mechanical  Drawing 4to,  4  oo 

Velocity  Diagrams 8vo,  i   50 

*  Mahan's  Descriptive  Geometry  and  Stone-cutting 8vo,  i   50 

Industrial  Drawing.     (Thompson.) 8vo,  3  50 

Mover's  Descriptive  Geometry.     (In  press.) 

Reed's  Topographical  Drawing  and  Sketching 4to,  5  oo 

Reid's  Course  in  Mechanical  Drawing 8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  oo 

Robinson's  Principles  of  Mechanism 8vo,  3  oo 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  oo 

Smith's  Manual  of  Topographical  Drawing.     (McMillan.) 8vo,  50 

Warren's  Elements  of  Plane  and  Solid  Free-hand  Geometrical  Drawing,  izmo,  oo 

Drafting  Instruments  and  Operations i2mo,  25 

Manual  of  Elementary  Projection  Drawing I2mo, 

Manual  of  Elementary  Problems  in  the  Linear  Perspective  of  Form  and 

Shadow 1 2mo,  oo 

Plane  Problems  in  Elementary  Geometry i2mo,  25 

Primary  Geometry i2mo,  75 

Elements  of  Descriptive  Geometry,  Shadows,  and  Perspective 8vo,  3  50 

General  Problems  of  Shades  and  Shadows 8vo,  3  oo 

Elements  of  Machine  Construction  and  Drawing 8vo,  7  50 

Problems,  Theorems,  and  Examples  in  Descriptive  Geometry 8vo,  2  50 

Weisbach's  Kinematics  and  Power  of  Transmission.    (Hermann  and  Klein  >8vo,  5  oo 

Whelpley's  Practical  Instruction  in  the  Art  of  Letter  Engraving i2mo,  2  oo 

Wilson's  (H.  M.)  Topographic  Surveying 8vo,  3  50 

Wilson's  (V.  T.)  Free-hand  Perspective 8vo,  2  50 

Wilson's  (V.  T. )  Free-hand  Lettering 8vo,  i   oo 

Woolf *s  Elementary  Course  in  Descriptive  Geometry.  .                         Large  8vo,  3  oo 


ELECTRICITY  AND   PHYSICS. 

Anthony  and  Brackett's  Text-book  of  Physics,     t  Magie. ) Small  8vo,  3  oo 

Anthony's  Lecture-notes  on  the  Theory  of  Electrical  Measurements    .  .  .  i2mo,  i   oo 

Benjamin's  History  of  Electricity 8vo,  3  oo 

Voltaic  Cell 8vo,  3  oo 

Classen's  Quantitative  Chemical  Analysis  by  Electrolysis.     (Boltwood. ).8vo,  3  oo 

Crehore  and  Squier's  Polarizing  Photo-chronograph.  ...                               .8vo,  3  oo 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book.  i6mo,  morocco,  5  oo 
Dolezalek's    Theory    of    the    Lead    Accumulator    (Storage    Battery).      (Von 

Ende.) i2mo,  2  50 

Duhem's  Thermodynamics  and  Chemistry.     (Burgess.  .                                 8vo,  4  oo 

Flather's  Dynamometers,  and  the  Measurement  of  Power.  .  .                      i2mo,  3  oo 

Gilbert's  De  Magnete.     (Mottelay.) 8vo,  2  50 

Hanchett's  Alternating  Currents  Explained i2mo,  i  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,  2  50 

Holman's  Precision  of  Measurements 8vo,  2  oo 

Telescopic    Mirror-scale  Method,  Adjustments,  and   Tests    .  .  .  Large  8vo,  75 

Kinzbrunner's  Testing  of  Continuous-Current  Machines.  ...                      .  .8vo.  2  oo 

Landauer's  Spectrum  Analysis.     (Tingle.  .  .  .                                                     8vo,  3  oo 

Le  Chatelien's  High-temperature  Measurements.  <  Boudouard  --Burgess. )  i2mo,  3  oo 

Lob's  Electrolysis  and  Electrosynthesis  of  Organic  Compounds.  (Lorenz.  >  i2mo,  i  oo 


*  Lyons's  Treatise  on  Electromagnetic  Phenomena.   Vols.  I.  and  II.  8vo,  each,  6  oo 

*  Michie's  Elements  of  Wave  Motion  Relating  to  Sound  and  Light 8vo,  4  oo 

Niaudet's  Elementary  Treatise  on  Electric  Batteries.     (Fishback.) i2mo,  2  50 

*  Rosenberg's  Electrical  Engineering.     (Haldane  Gee — Kinzbrunner.).  .    8vo, 

Ryan,  Norris,  and  Hoxie's  Electrical  Machinery.     Vol.  1 8vo, 

Thurston's  Stationary  Steam-engines 8vo, 

*  Tillman's  Elementary  Lessons  in  Heat 8vo, 

Tory  and  Pitcher's  Manual  of  Laboratory  Physics Small  8vo, 

Ulke's  Modern  Electrolytic  Copper  Refining 8vo,  3  oo 

LAW. 

*  Davis's  Elements  of  Law 8vo,  2  50 

*  Treatise  on  the  Military  Law  of  United  States 8vo,  7  oo 

Sheep,  7  50 

Manual  for  Courts-martial i6mo,  morocco,  i   50 

Wait's  Engineering  and  Architectural  Jurisprudence 8vo,  6  oo 

Sheep,  6  50 

Law  of  Operations  Preliminary  to  Construction  in  Engineering  and  Archi- 
tecture  8vo,  5  oo 

Sheep,  5  50 

Law  of  Contracts 8vo,  3  oo 

Winthrop's  Abridgment  of  Military  Law 12010,  2  50 

MANUFACTURES. 

Bernadou's  Smokeless  Powder — Nitro-cellulose  and  Theory  of  the  Cellulose 

Molecule I2mo,  2  50 

Holland's  Iron  Founder i2mo,  2  50 

"  The  Iron  Founder,"  Supplement i2mo,  2  50 

Encyclopedia  of  Founding  and  Dictionary  of  Foundry  Terms  Used  in  the 

Practice  of  Moulding i2mo,  3  oo 

Eissler's  Modern  High  Explosives 8vo,  4  oo 

Effront's  Enzymes  and  their  Applications.     (Prescott.) 8vo,  3  oo 

Fitzgerald's  Boston  Machinist zamo,  i  oo 

Ford's  Boiler  Making  for  Boiler  Makers i8mo,  i   oo 

Hopkin's  Oil-chemists'  Handbook 8vo,  3  oo 

Keep's  Cast  Iron 8vo,  2  50 

Leach's  The  Inspection  and  Analysis  of  Food  with  Special  Reference  to  State 

Control Large  8vo,  7  50 

Matthews's  The  Textile  Fibres 8vo,  3  50 

Metcalf  s  Steel.     A  Manual  for  Steel-users i2mo,  2  oo 

Metcalfe's  Cost  of  Manufactures — And  the  Administration  of  Workshops. 8vo,  5  oo 

Meyer's  Modern  Locomotive  Construction 4to,  10  oo 

Morse's  Calculations  used  in  Cane-sugar  Factories i6mo,  morocco,  i   50 

*  Reisig's  Guide  to  Piece-dyeing 8vo,  25  oo 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Smith's  Press-working  of  Metals 8vo,  3  oo 

Spalding's  Hydraulic  Cement i2mo,  2  oo 

Spencer's  Handbook  for  Chemists  of  Beet-sugar  Houses.     .    .   i6mo,  morocco,  3  oo 

Handbook  for  Sugar  Manufacturers  and  their  Chemists    .  i6mo,  morocco,  a  oo 

Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced 8vo,  5  oo 

Thurston's  Manual  of  Steam-boilers,  their  Designs,  Construction  and  Opera- 
tion. ...                           8vo,  5  oo 

*  Walke's  Lectures  on  Explosives 8vo,  4  oo 

Ware's  Manufacture  of  Sugar.     (In  press.) 

West's  American  Foundry  Practice i2mo,  2  50 

Moulder's  Text-book 12010,  2  50 

10 


Wolff's  Windmill  as  a  Prime  Mover 8vo,    3  oo 

Wood's  Rustless  Coatings:   Corrosion  and  Electrolysis  of  Iron  and  Steel.  .8vo,    4  oo 


MATHEMATICS. 

Baker's  Elliptic  Functions 8vo,     i   50 

*  Bass's  Elements  of  Differential  Calculus 12010,    4  oo 

Briggs's  Elements  of  Plane  Analytic  Geometry i2mo, 

Compton's  Manual  of  Logarithmic  Computations i2mo, 

Davis's  Introduction  to  the  Logic  of  Algebra 8vo, 

*  Dickson's  College  Algebra Large  tamo, 


*       Introduction  to  the  Theory  of  Algebraic  Equations Large  12 mo, 

Emch's  Introduction  to  Protective  Geometry  and  its  Applications 8vo, 

Halsted's  Elements  of  Geometry 8vo, 

Elementary  Synthetic  Geometry 8vo, 


oo 
So 
50 
50 
25 
50 
75 
50 
Rational  Geometry i2mo,  75 

*  Johnson's  (J.  B.)  Three-place  Logarithmic  Tables:    Vest-pocket  size. paper,         15 

100  copies  for     5  oo 

Mounted  on  heavy  cardboard,  8X  10  inches,         25 
10  copies  for     2  oo 

Johnson's  (W.  W.)  Elementary  Treatise  on  Differential  Calculus    .  Small  8vo,    3  oo 
Johnson's  (W.  W.)  Elementary  Treatise  on  the  Integral  Calculus. Small  8vo,     i  50 

Johnson's  (W.  W.)  Curve  Tracing  in  Cartesian  Co-ordinates i2mo,     i  oo 

Johnson's  (W.  W.)  Treatise  on  Ordinary  and  Partial  Differential  Equations. 

SmallSvo,    3  50 
Johnson's  (W.  W.)  Theory  of  Errors  and  the  Method  of  Least  Squares.  12010,     i  50 

*  Johnson's  (W.  W.)  Theoretical  Mechanics i2mo,    3  oo 

Laplace's  Philosophical  Essay  on  Probabilities.     (Truscott  and  Emory. ) .  i2mo,     2  oo 

*  Ludlow  and  Bass.     Elements  of  Trigonometry  and  Logarithmic  and  Other 

Tables 8vo,    3  oo 

Trigonometry  and  Tables  published  separately Each,    2  oo 

*  Ludlow's  Logarithmic  and  Trigonometric  Tables 8vo,     i  oo 

Maurer's  Technical  Mechanics 8.    ,    400 

Merriman  and  Woodward's  Higher  Mathematics 8vo,    5  oo 

Merriman's  Method  of  Least  Squares 8vo,     2  oo 

Rice  and  Johnson's  Elementary  Treatise  on  the  Differential  Calculus. .  Sm.  8vo,    3  o« 

Differential  and  Integral  Calculus.     2  vols.  in  one Small  8vo,     2  50 

Wood's  Elements  of  Co-ordinate  Geometry 8vo,     2  oo 

Trigonometry:   Analytical,  Plane,  and  Spherical i2mo,     i  oo 


MECHANICAL  ENGINEERING. 

MATERIALS  OF  ENGINEERING,  STEAM-ENGINES  AND  BOILERS. 

Bacon's  Forge  Practice i2mo,  i   50 

Baldwin's  Steam  Heating  for  Buildings i2mo,  2  50 

Barr's  Kinematics  of  Machinery 8vo,  2  50 

*  Bartlett's  Mechanical  Drawing 8vo,  3  oo 

*  "  "  "         Abridged  Ed.  .  8vo,     i   50 

Benjamin's  Wrinkles  and  Recipes i2mo,     2  oo 

Carpenter's  Experimental  Engineering .  .8vo,    6  oo 

Heating  and  Ventilating  Buildings 8vo,    4  oo 

Gary's  Smoke  Suppression  in  Plants  using  Bituminous  Coal.     'In  Prepara- 
tion.) 

Clerk's  Gas  and  Oil  Engine Small  8vo,     4  oo 

Coolidge's  Manual  of  Drawing 8vo,  paper,     i   oo 

Coolidge  and  Freeman's  Elements  of  General  Drafting  for  Mechanical  En- 
gineers  Oblong  4to,    2  50 

11 


Cromwell's  Treatise  on  Toothed  Gearing i2mo,  i   50 

Treatise  on  Belts  and  Pulleys.     .  i2mo,  i  50 

Durley's  Kinematics  of  Machines 8vo,  4  oo 

Flather's  Dynamometers  and  the  Measurement  of  Power i2mo,  3  oo 

Rope  Driving i2mo,  2  oo 

Gill's  Gas  and  Fuel  Analysis  for  Engineers i2mo,  i   25 

Hall's  Car  Lubrication i2mo,  i  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors' i6mo,  morocco,  2  50 

Button's  The  Gas  Engine 8vo,  5  oo 

Jamison's  Mechanical  Drawing 8vo,  2  50 

Jones's  Machine  Design: 

Part  I.     Kinematics  of  Machinery 8vo,  i   50 

Part  II.     Form,  Strength,  and  Proportions  of  Parts.  . 8vo,  3  oo 

Kent's  Mechanical  Engineers'  Pocket-book i6mo,  morocco,  5  oo 

Kerr's  Power  and  Power  Transmission 8vo,  2  oo 

Leonard's  Machine  Shop,  Tools,  and  Methods.     (In  press,  i 

Lorenz's  Modern  Refrigerating  Machinery.     (Pope,  Baven,  and  Dean.)     (In  press.  - 

MacCord's  Kinematics;   or,  Practical  Mechanism 8vo,  5  oo 

Mechanical  Drawing 4to,  4  oo 

Velocity  Diagrams 8vo,  i   50 

Mahan's  Industrial  Drawing.      (Thompson.) 8vo,  3  50 

Poole's  Calorific  Power  of  Fuels 8vo,  3  oo 

Reid's  Course  in  Mechanical  Drawing 8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design  8vo,  3  oo 

Richard's  Compressed  Air 12010,  i   50 

Robinson's  Principles  of  Mechanism 8vo,  3  oo 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  oo 

Smith's  Press-working  of  Metals 8vo,  3  oo 

Thurston's    Treatise    on    Friction  and    Lost    Work    in    Machinery   and    Mill 

Work 8vo,  3  oo 

Animal  as  a  Machine  and  Prime  Motor,  and  the  Laws  of  Energetics .  1 2010,  i   oo 

Warren's  Elements  of  Machine  Construction  and  Drawing 8vo,  7  50 

Weisbach's    Kinematics    and    the    Power    of    Transmission.      (Berrmann — 

Klein. ) 8vo,  5  oo 

Machinery  of  Transmission  and  Governors.     (Berrmann — Klein.).  .  8vo,  5  oo 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  3  oo 

Wood's  Turbines 8vo,  2  50 


MATERIALS   OF    ENGINEERING. 

Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering.     6th  Edition. 

Reset 8vD,  7  50 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

Johnson's  Materials  of  Construction 8vo,  6  oo 

Keep's  Cast  Iron 8vo,  2  50 

Lanza's  Applied  Mechanics 8vo,  7  50 

Martens's  Bandbook  on  Testing  Materials.     (Benning.) 8vo,  7  50 

Merriman's  Text-book  on  the  Mechanics  of  Materials 8vo,  4  oo 

Strength  of  Materials i2mo,  i   oo 

Metcalf's  Steel.     A  manual  for  Steel-users i2mo.  2  oo 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Smith's  Materials  of  Machines i2mo,  i   oo 

Thurston's  Materials  of  Engineering 3  vols.,  8vo,  8  oo 

Part  II.     Iron  and  Steel ,  -8vo,  3  50 

Part  III.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents .8vo,  250 

Text-book  of  the  Materials  of  Construction 8vo,  5  oo 

12 


Wood's  (De  V.)  Treatise  on  the  Resistance  of  Materials  a,,    -n  Appendix  on 

the  Presentation  of  Timber 8vo,    2  oo 

Wood's  (De  V.)  Elements  of  Analytical  Mechanics 8vo,    3  oo 

Wood's  (M.  P.)  Rustless  Coatings:    Corrosion  and  Electrolysis  of  Iron  and 

SteeL 8vo,    4  oo 


STEAM-ENGINES  AND  BOILERS. 


Berry's  Temperature-entropy  Diagram I2mo,  i  25 

Carnot's  Reflections  on  the  Motive  Power  of  Heat.     (Thurston.) 12 mo,  i  50 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book.  .  .  .  i6mo,  mor.,  5  oo 

Ford's  Boiler  Making  for  Boiler  Makers i8mo,  i  oo 

Goss's  Locomotive  Sparks. 8vo,  2  oo 

Hemenway's  Indicator  Practice  and  Steam-engine  Economy i2mo,  2  oo 

Button's  Mechanical  Engineering  of  Power  Plants 8vo,  5  oo 

Heat  and  Heat-engines 8vo,  5  oo 

Kent's  Steam  boiler  Economy 8vo,  4  oo 

Kneass's  Practice  and  Theory  of  the  Injector 8vo,  i  50 

MacCord's  Slide-valves 8vo,  2  oo 

Meyer's  Modern  Locomotive  Construction 4to,  10  oo 

Peabody's  Manual  of  the  Steam-engine  Indicator 12 mo.  i   50 

Tables  of  the  Properties  of  Saturated  Steam  and  Other  Vapors 8vo,  i  oo 

Thermodynamics  of  the  Steam-engine  and  Other  Heat-engines 8vo,  5  oo 

Valve-gears  for  Steam-engines 8vo,  2  50 

Peabody  and  Miller's  Steam-boilers 8vo,  4  oo 

Pray's  Twenty  Years  with  the  Indicator Large  8vo,  2  50 

Pupin's  Thermodynamics  of  Reversible  Cycles  in  Gases  and  Saturated  Vapors. 

(Osterberg.) : i2mo,  i   25 

Reagan's  Locomotives:   Simple   Compound,  and  Electric i2mo,  2  50 

Rontgen's  Principles  of  Thermodynamics.     (Du  Bois. ) 8vo,  5  oo 

Sinclair's  Locomotive  Engine  Running  and  Management i2mo,  2  oo 

Smart's  Handbook  of  Engineering  Laboratory  Practice i2mo,  2  50 

Snow's  Steam-boiler  Practice 8vo,  3  oo 

Spangler's  Valve-gears 8vo,  2  50 

Notes  on  Thermodynamics 1 2mo,  i  oo 

Spangler,  Greene,  and  Marshall's  Elements  of  Steam-engineering  . 8vo,  3  oo 

Thurston's  Handy  Tables 8vo.  i  50 

Manual  of  the  Steam-engine 2  vols.,  8vo,  10  oo 

Part  I.     History,  Structure,  and  Theory 8vo,  6  oo 

Part  II.     Design,  Construction,  and  Operation 8vo,  6  oo 

Handbook  of  Engine  and  Boiler  Trials,  and  the  Use  of  the  Indicator  and 

the  Prony  Brake 8vo,  5  oo 

Stationary  Steam-engines 8vo.  2  50 

Steam-boiler  Explosions  in  Theory  and  in  Practice    12010,  i  50 

Manual  of  Steam-boilers,  their  Designs,  Construction,  and  Operation Cvo.  5  oo 

Weisbach's  Heat,  Steam,  and  Steam-engines.     (Du  Bois.  > 8vo,  5  oo 

Whitham's  Steam-engine  Design 8vo,  5  oo 

Wilson's  Treatise  on  Steam-boilers.     (Flather.) i6rao,  2  50 

Wood's  Thermodynamics,  Heat  Motors,  and  Refrigerating  Machines ...  8vo,  4  oo 


MECHANICS  AND  MACHINERY. 

Barr's  Kinematics  of  Machinery 8vo,  2  50 

Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Chase's  The  Art  of  Pattern-making i2mo,  2  50 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

13 


Church's  Notes  and  Examples  in  Mechanics 8vo,  2  oo 

Compton's  First  Lessons  in  Metal-working i2mo;  i  50 

Compton  and  De  Groodt's  The  Speed  Lathe i2mo,  i   50 

Cromwell's  Treatise  on  Toothed  Gearing i2mo,  :  50 

Treatise  on  Belts  and  Pulleys i2mo,  i  50 

Dana's  Text-book  of  Elementary  Mechanics  for  Colleges  and  Schools.  .  i2mo,  i  50 

Dingey's  Machinery  Pattern  Making i2mo,  2  oo 

Dredge's   Record  of   the   Transportation   Exhibits   Building   of   the   World's 

Columbian  Exposition  of  1893 4to  half  morocco,  5  oo 

Du  Bois's  Elementary  Principles  of  Mechanics: 

Vol.      I.     Kinematics 8vo,  3  So 

Vol.    II.     Statics * 8vo,  4  oo 

VoL  III.     Kinetics 8vo,  3  50 

Mechanics  of  Engineering.     Vol.    I Small  4to,  7  5<> 

VoL  II Small  4to,  10  oo 

Durley's  Kinematics  of  Machines 8vo,  4  oo 

Fitzgerald's  Boston  Machinist i6mo,  i  oo 

Flather's  Dynamometers,  and  the  Measurement  of  Power i2mo,  3  oo 

Rope  Driving i2mo,  2  oo 

Goss's  Locomotive  Sparks 8vo,  2  oo 

Hall's  Car  Lubrication i2mo,  i  oo 

Holly's  Art  of  Saw  Filing i8mo,  75 

James's  Kinematics  of  a  Point  and  the  Rational  Mechanics  of  a  Particle.     (In  press.) 

*  Johnson's  (W.  W.)  Theoretical  Mechanics I2mo,  3  oo 

Johnson's  (L.  J. )  Statics  by  Graphic  and  Algebraic  Methods 8vo,  2  oo 

Jones's  Machine  Design:  • 

Part    I.     Kinematics  of  Machinery 8vo,  i  50 

Part  II.     Form,  Strength,  and  Proportions  of  Parts 8vo,  3  oo 

Kerr's  Power  and  Power  Transmission 8vo,  2  oo 

Lanza's  Applied  Mechanics 8vo,  7  50 

Leonard's  Machine  Shop,  Tools,  and  Methods.     (In  press.) 

Lorenz's  Modern  Refrigerating  Machinery.      (Pope,  Haven,  and  Dean.)      (In  press.) 

MacCord's  Kinematics;   or,  Practical  Mechanism 8vo,  5  oo 

Velocity  Diagrams 8vo,  i  50 

Maurer's  Technical  Mechanics 8vo,  4  oo 

Merriman's  Text-book  on  the  Mechanics  of  Materials 8vo,  4  oo 

*  Elements  of  Mechanics i2mo,  i  oo 

*  Michie's  Elements  of  Analytical  Mechanics 8vo,  4  oo 

Reagan's  Locomotives:   Simple,  Compound,  and  Electric 12010,  2  50 

Reid's  Course  in  Mechanical  Drawing 8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo.  3  oo 

Richards's  Compressed  Air 12 mo,  i   50 

Robinson's  Principles  of  Mechanism 8vo,  3  co 

Ryan,  Norris,  and  Hoxie's  Electrical  Machinery.     Vol.  1 8vo,  2  50 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  oo 

Sinclair's  Locomotive-engine  Running  and  Management 12010,  2  oo 

Smith's  (O.)  Press-working  of  Metals 8vo.  3  oo 

Smith's  (A.  W.)  Materials  of  Machines i2mo.  i  oo 

Spangler,  Greene,  and  Marshall's  Elements  of  Steam-engineering 8vo,  3  oo 

Thurston's  Treatise  on   Friction  and   Lost  V/ork   in     Machinery  and    Mill 

Work 8vo.  3  oo 

Animal  as  a  Machine  and  Prime  Motor,  and  the  Lawc  of  Energetics 

i2mo,  i  oo 

Warren's  Elements  of  Machine  Construction  and  Drawing 8vo,  7  50 

Weisbach's  Kinematics  and  Power  of  Transmission.    (Herrmann  —  Klein.  ).8vo,    5  oo 

Machinery  of  Transmission  and  Governors.       (  Herrmann  —Klein. ).8vo,  5  oo 

Wood's  Elements  of  Analytical  Mechanics.                    8vo.  3  oo 

Principles  of  Elementary  Mechanics.  .  .              12010,  i   25 

Turbines 8vo .  2  50 

The  World's  Columbian  Exposition  of  1893 4*0,  i  oo 

14 


METALLURGY. 

Egleston's  Metallurgy  of  Silver,  Gold,  and  Mercury: 

VoL    I.     Silver 8vo,  7  50 

VoL  II.     Gold  and  Mercury 8vo,  7  50 

**  Iles's  Lead-smelting.     (Postage  p  cents  additional.) i2mo,  2  50 

Keep's  Cast  Iron 8vo,  2  50 

Kunhardt's  Practice  of  Ore  Dressing  in  Europe 8vo,  i  50 

Le  Cbatelier's  High-temperature  Measuremepts.  (Boudouard — Burgess. )i2mo,  3  oo 

Metcalf's  SteeL     A  Manual  for  Steel-users     i2mo,  2  oo 

Smith's  Materials  of  Machines i2mo,  i  oo 

Thurston's  Materials  of  Engineering.     In  Three  Parts 8vo,  8  oo 

Part    II.     Iron  and  Steel 8vo.  3  50 

Part  HI.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,  2  50 

Ulke's  Modern  Electrolytic  Copper  Refining 8vo,  3  oo 

MINERALOGY. 

Barringer's  Description  of  Minerals  of  Commercial  Value.    Oblong,  morocco,  2  50 

Boyd's  Resources  of  Southwest  Virginia 8vo,  3  oo 

Map  of  Southwest  Virignia Pocket-book  form.  2  oo 

Brush's  Manual  of  Determinative  Mineralogy.     (Penfi>ld.) 8vo,  4  oo 

Chester's  Catalogue  of  Minerals 8vo,  paper,  i  oo 

Cloth,  i  25 

Dictionary  of  the  Names  of  Minerals 8vo,  3  50 

Dana's  System  of  Mineralogy Large  8vo,  half  leather,  12  50 

First  Appendix  to  Dana's  New  "  System  of  Mineralogy." Large  8vo,  i  oo 

Text-book  of  Mineralogy 8vo,  4  oo 

Minerals  and  How  to  Study  Them i2mo,  i  50 

Catalogue  of  American  Localities  of  Minerals Large  8vo,  i  oo 

Manual  of  Mineralogy  and  Petrography i2mo  2  oo 

Douglas's  Untechnical  Addresses  on  Technical  Subjects 12 mo,  i  oo 

Eakle's  Mineral  Tables 8vo,  i  25 

Egleston's  Catalogue  of  Minerals  and  Synonyms 8vo.  2  50 

Hussak's  The  Determination  of  Rock-forming  Minerals.    (Smith.)  .Small  8vo,  2  oo 

Merrill's  Non-metallic  Minerals:   Their  Occurrence  and  Uses 8vo,  4  oo 

*  Penfield's  Notes  on  Determinative  Mineralogy  and  Record  of  Mineral  Tests. 

8vo  paper,  o  50 
Rosenbusch's    Microscopical   Physiography   of    the    Rock-maki»g  Minerals 

(Iddings.) 8vo.  5  oo 

*  Tillman  s  Text-book  of  Important  Minerals  and  Rocks ...    .8vo.  2  oo 

Williams's  Manual  of  Lithology 8vo,  3  oo 

MINING. 

Beard's  Ventilation  of  Mines I2mo.  2  50 

Boyd's  Resources  of  Southwest  Virginia 8vo,  3  oo 

Map  of  Southwest  Virginia Pocket  book  form.  2  oo 

Douglas's  Untechnical  Addresses  on  Technical  Subjects i2mo.  i  oo 

*  Drinker's  Tunneling,  Explosive  Compounds,  and  Rock  Drills     4to.hf  mor  25  oo 

Eissler's  Modern  High  Explosives 8vo  4  oo 

Fowler's  Sewage  Works  Analyses 12010  2  oo 

Goodyear's  Coal-mines  of  the  Western  Coast  of  the  United  States       .      12 mo  2  50 

Ihlseng's  Manual  of  Mining 8vo.  5  oo 

**  Iles's  Lead-smelting.     (Postage  QC.  additional.) I2mo.  2  50 

Kunhardt's  Practice  of  Ore  Dressing  in  Europe 8vo.  i   50 

O'Driscoll's  Notes  on  the  Treatment  of  Gold  Ores 8vo.  2  oo 

*  Walke's  Lectures  on  Explosives '.    8vo.  4  oo 

Wilson's  Cyanide  Processes I2mo,  i  50 

Chlorination  Process I2mo,  i  50 

15 


Wilson's  Hydraulic  and  Placer  Mining iimo,     2 

Treatise  on  Practical  and  Theoretical  Mine  Ventilation T2mo.     i 

SANITARY  SCIENCE. 

Folwell's  Sewerage.     (Designing,  Construction,  and  Maintenance.) 8vo,  3 

Water-supply  Engineering 8vo,  4 

Fuertes's  Water  and  Public  Health i2mo,  i 

Water-filtration  Works i2mo!  2 

Gerhard's  Guide  to  Sanitary  House-inspection i6mo,  i 

Goodrich's  Economic  Disposal  of  Town's  Refuse DemySvo, 

Hazen's  Filtration  of  Public  Water-supplies 8vo, 

Leach's  The  Inspection  and  Analysis  of  Food  with  Special  Reference  to  State 

Control 8vo,  7 

Mason's  Water-supply.  (Considered  principally  from  a  Sanitary  Standpoint)  8vo,  4 

Examination  of  Water.     (Chemical  and  Bacteriological.) i2mo,  i 

Merriman's  Elements  of  Sanitary  Engineering 8vo,  2 

Ogden's  Sewer  Design I2mo,  2 

Prescott  and  Winslow's  Elements  of  Water  Bacteriology,  with  Special  Refer- 
ence to  Sanitary  Water  Analysis I2mo,  i 

*  Price's  Handbook  on  Sanitation I2mo,  i 

Richards's  Cost  of  Food.     A  Study  in  Dietaries i2mo,  i 

Cost  of  Living  as  Modified  by  Sanitary  Science I2mo,  i 

Richards  and  Woodman's  Air,  Water,  and   Food  from  a  Sanitary  Stand- 
point  8vo,  2 

*  Richards  and  Williams's  The  Dietary  Computer 8vo,  i 

Rideal's  Sewage  and  Bacterial  Purification  of  Sewage 8vo,  3 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5 

Von  Behring's  Suppression  of  Tuberculosis.     (Bolduan.) i2mo,  i 

Whipple's  Microscopy  of  Drinking-water 8vo,  3 

WoodhulPs  Notes  on  Military  Hygiene i6mo,  i 

MISCELLANEOUS. 

De  Fursac's  Manual  of  Psychiatry.     (Rosanoff  and  Collins.).  .  .  .Large  i2mo,     2 
Emmons's  Geological  Guide-book  of  the  Rocky  Mountain  Excursion  of  the 

International  Congress  of  Geologists Large  8vo,     i 

Ferrel's  Popular  Treatise  on  the  Winds 8vo. 

Haines's  American  Railway  Management i2mo,     2 

i'ott's  Composition,  Digestibility,  and  Nutritive  Value  of  Food.   Mounted  chart,     i 

Fallacy  of  the  Present  Theory  of  Sound i6mo,     i 

Ricketts's  History  of  Rensselaer  Polytechnic  Institute,  1824-1894.  .Small  8vo, 

Rostoski's  Serum  Diagnosis.     (Bolduan.) i2mo, 

Rotherham's  Emphasized  New  Testament Large  8vo, 

Steel's  Treatise  on  the  Diseases  of  the  Dog 8vo, 

Totten's  Important  Question  in  Metrology 8vo. 

The  World's  Columbian  Exposition  of  1893 4to, 

Von  Behring's  Suppression  of  Tuberculosis.     (Bolduan.) I2mo,     i 

Winslow's  Elements  of  Applied  Microscopy i2mo,     i 

Worcester  and  Atkinson.      Small  Hospitals,  Establishment  and  Maintenance; 

Suggestions  for  Hospital  Architecture :  Plans  for  Small  Hospital .  1 2mo,     i 

HEBREW  AND   CHALDEE  TEXT-BOOKS. 

Green's  Elementary  Hebrew  Grammar izmo,  i 

Hebrew  Chrestomathy tfvo,  2 

Gesenius's  Hebrew  and   Chaldee   Lexicon  to  the  Old  Testament  Scriptures. 

(Tregelles. ) Small  4to,  half  morocco,  5 

Lettem's  Hebrew  Bible 8vo,  2 

16 


14  DAY  USE 

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